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Volumn 8, Issue 2, 2002, Pages 469-513

Controllability of partial differential equations and its semi-discrete approximations

Author keywords

Controllability; Finite differences; Galerkin method; Heat equation; Navier Stokes equations; Semi discrete approximations; Wave equation

Indexed keywords


EID: 0038100523     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2002.8.469     Document Type: Article
Times cited : (69)

References (158)
  • 1
    • 0002379257 scopus 로고
    • Non unicité du problème de Cauchy
    • S. Alinhac, Non unicité du problème de Cauchy. Annals of Mathematics 117 (1983), 77-108.
    • (1983) Annals of Mathematics , vol.117 , pp. 77-108
    • Alinhac, S.1
  • 2
    • 0030518431 scopus 로고    scopus 로고
    • Bloch wave homogenization for a spectral problem in fluid-solid structures
    • G. Allaire, C. Conca, Bloch wave homogenization for a spectral problem in fluid-solid structures. Arch. Rat. Mech. Anal. 135(3) (1996), 197-257.
    • (1996) Arch. Rat. Mech. Anal. , vol.135 , Issue.3 , pp. 197-257
    • Allaire, G.1    Conca, C.2
  • 3
    • 0031994541 scopus 로고    scopus 로고
    • Bloch wave homogenization and spectral asymptotic analysis
    • G. Allaire, C. Conca, Bloch wave homogenization and spectral asymptotic analysis. J. Math. Pures Appl. 77 (1998), 153-208.
    • (1998) J. Math. Pures Appl. , vol.77 , pp. 153-208
    • Allaire, G.1    Conca, C.2
  • 4
    • 0001480947 scopus 로고    scopus 로고
    • Contrôle analytique de l'équation des ondes et de l'équation de Schrödinger sur des surfaces de révolution
    • B. Allibert, Contrôle analytique de l'équation des ondes et de l'équation de Schrödinger sur des surfaces de révolution. Comm. P. D. E. 23(1&2) (1998), 1493-1556.
    • (1998) Comm. P. D. E. , vol.23 , Issue.1-2 , pp. 1493-1556
    • Allibert, B.1
  • 5
    • 84996134669 scopus 로고    scopus 로고
    • Geometrical aspects of exact boundary controllability of the wave equation. A numerical study
    • M. Asch, G. Lebeau, Geometrical aspects of exact boundary controllability of the wave equation. A numerical study. ESAIM: COCV 3 (1998), 163-212.
    • (1998) ESAIM: COCV , vol.3 , pp. 163-212
    • Asch, M.1    Lebeau, G.2
  • 7
    • 0000477543 scopus 로고
    • Contrôlabilité exacte, homogénéisation et localisation d'ondes dans un milieu non-homogène
    • M. Avellaneda, C. Bardos, J. Rauch, Contrôlabilité exacte, homogénéisation et localisation d'ondes dans un milieu non-homogène, Asymptotic Analysis 5 (1992), 481-494.
    • (1992) Asymptotic Analysis , vol.5 , pp. 481-494
    • Avellaneda, M.1    Bardos, C.2    Rauch, J.3
  • 8
    • 84996143960 scopus 로고    scopus 로고
    • Exact controllability of the superlinear heat equation
    • to appear
    • V. Barbu, Exact controllability of the superlinear heat equation, Appl. Math. Optim., to appear.
    • Appl. Math. Optim.
    • Barbu, V.1
  • 9
    • 0026923885 scopus 로고
    • Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary
    • C. Bardos, G. Lebeau, J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary. SIAM J. Cont. Optim. 30 (1992), 1024-1065.
    • (1992) SIAM J. Cont. Optim. , vol.30 , pp. 1024-1065
    • Bardos, C.1    Lebeau, G.2    Rauch, J.3
  • 11
    • 85039387552 scopus 로고    scopus 로고
    • Ph. D. dissertation, Universidade Federal do Rio de Janeiro, July
    • S. Bezerra, Ph. D. dissertation, Universidade Federal do Rio de Janeiro, July, 1999.
    • (1999)
    • Bezerra, S.1
  • 12
    • 27844449058 scopus 로고    scopus 로고
    • Contrôle de l'équation des ondes dans des ouverts peu réguliers
    • N. Burq, Contrôle de l'équation des ondes dans des ouverts peu réguliers. Asymptotic Analysis 14 (1997), 157-191.
    • (1997) Asymptotic Analysis , vol.14 , pp. 157-191
    • Burq, N.1
  • 13
    • 0000469955 scopus 로고    scopus 로고
    • Condition nécessaire et suffisante pour la contrô labilité exacte des ondes
    • N. Burq, P. Gérard, Condition nécessaire et suffisante pour la contrôlabilité exacte des ondes. C. R. Acad. Sci. Paris 325 (1997), 749-752.
    • (1997) C. R. Acad. Sci. Paris , vol.325 , pp. 749-752
    • Burq, N.1    Gérard, P.2
  • 14
    • 0035536763 scopus 로고    scopus 로고
    • Null controllability in unbounded domains for the semilinear heat equation with nonlinearities involving gradient terms
    • V. Cabanillas, S. de Menezes, E. Zuazua, Null controllability in unbounded domains for the semilinear heat equation with nonlinearities involving gradient terms. J. Optim. Theory Applications 110(2) (2001).
    • (2001) J. Optim. Theory Applications , vol.110 , Issue.2
    • Cabanillas, V.1    De Menezes, S.2    Zuazua, E.3
  • 15
    • 0012966638 scopus 로고    scopus 로고
    • Boundary controllability of the one-dimensional wave equation with rapidly oscillating density
    • C. Castro, Boundary controllability of the one-dimensional wave equation with rapidly oscillating density. Asymptotic Analysis 20 (1999), 317-350.
    • (1999) Asymptotic Analysis , vol.20 , pp. 317-350
    • Castro, C.1
  • 17
    • 0032164347 scopus 로고    scopus 로고
    • Controllability of a hybrid system consisting of two flexible beams connected by a point mass
    • C. Castro, E. Zuazua, Controllability of a hybrid system consisting of two flexible beams connected by a point mass. SIAM J. Cont. Optim. 36(5) (1998), 1576-1595.
    • (1998) SIAM J. Cont. Optim. , vol.36 , Issue.5 , pp. 1576-1595
    • Castro, C.1    Zuazua, E.2
  • 18
    • 0031164763 scopus 로고    scopus 로고
    • Contrôle de l'équation des ondes à densité rapidement oscillante à une dimension d'espace
    • C. Castro, E. Zuazua, Contrôle de l'équation des ondes à densité rapidement oscillante à une dimension d'espace. C. R. Acad. Sci. Paris 324 (1997), 1237-1242.
    • (1997) C. R. Acad. Sci. Paris , vol.324 , pp. 1237-1242
    • Castro, C.1    Zuazua, E.2
  • 19
    • 0033697984 scopus 로고    scopus 로고
    • Low frequency asymptotic analysis of a string with rapidly oscillating density
    • C. Castro, E. Zuazua, Low frequency asymptotic analysis of a string with rapidly oscillating density. SIAM J. Appl. Math. 60 (2000), 1205-1233.
    • (2000) SIAM J. Appl. Math. , vol.60 , pp. 1205-1233
    • Castro, C.1    Zuazua, E.2
  • 20
    • 0025399487 scopus 로고
    • On the propagation of confined waves along the geodesics
    • T. Cazenave, On the propagation of confined waves along the geodesics. J. Math. Anal. Appl. 146 (1990), 591-603.
    • (1990) J. Math. Anal. Appl. , vol.146 , pp. 591-603
    • Cazenave, T.1
  • 21
    • 0030265098 scopus 로고    scopus 로고
    • Exact controllability for semilinear parabolic equations with Neumann boundary conditions
    • D. Chac, O. Yu. Imanuvilov, S. M. Kim, Exact controllability for semilinear parabolic equations with Neumann boundary conditions. J. of Dynamical and Control Systems 2 (1996), 449-483.
    • (1996) J. of Dynamical and Control Systems , vol.2 , pp. 449-483
    • Chac, D.1    Imanuvilov, O.Yu.2    Kim, S.M.3
  • 22
    • 0001169464 scopus 로고
    • Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain
    • G. Chen, Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain. J. Math. Pures Appl. 58 (1979), 249-274.
    • (1979) J. Math. Pures Appl. , vol.58 , pp. 249-274
    • Chen, G.1
  • 23
    • 3042566290 scopus 로고
    • Exact boundary controllability for the wave equation in domains with small holes
    • D. Cioranescu, P. Donato, E. Zuazua, Exact boundary controllability for the wave equation in domains with small holes. J. Math. Pures et Appl. 71 (1992), 343-377.
    • (1992) J. Math. Pures et Appl. , vol.71 , pp. 343-377
    • Cioranescu, D.1    Donato, P.2    Zuazua, E.3
  • 24
    • 0031352502 scopus 로고    scopus 로고
    • Homogenization of periodic structures via Bloch decompositions
    • C. Conca, M. Vanninathan, Homogenization of periodic structures via Bloch decompositions. SIAM J. Math. Anal. 57(6) (1997), 1639-1656.
    • (1997) SIAM J. Math. Anal. , vol.57 , Issue.6 , pp. 1639-1656
    • Conca, C.1    Vanninathan, M.2
  • 25
    • 21344491639 scopus 로고
    • Asymptotic analysis of a multidimensional vibrating structure
    • C. Conca, E. Zuazua, Asymptotic analysis of a multidimensional vibrating structure. SIAM J. Math. Anal. 25(3) (1994), 836-858.
    • (1994) SIAM J. Math. Anal. , vol.25 , Issue.3 , pp. 836-858
    • Conca, C.1    Zuazua, E.2
  • 26
    • 0027624551 scopus 로고
    • Decay of solutions of the wave equation in a star-shaped domain with nonlinear boundary feedback
    • F. Conrad, B. Rao, Decay of solutions of the wave equation in a star-shaped domain with nonlinear boundary feedback. Asymptotic Anal. 7 (1993), 159-177.
    • (1993) Asymptotic Anal. , vol.7 , pp. 159-177
    • Conrad, F.1    Rao, B.2
  • 27
    • 0000731294 scopus 로고    scopus 로고
    • On the controllability of 2-D incompressible perfect fluids
    • J.-M. Coron, On the controllability of 2-D incompressible perfect fluids. J. Maths Pures Appl. 75(2) (1996), 155-188.
    • (1996) J. Maths Pures Appl. , vol.75 , Issue.2 , pp. 155-188
    • Coron, J.-M.1
  • 28
    • 84996141899 scopus 로고    scopus 로고
    • On the controllability of the 2-D incompressible Navier Stokes equations with the Navier slip boundary conditions
    • J.-M. Coron, On the controllability of the 2-D incompressible Navier Stokes equations with the Navier slip boundary conditions. ESAIM: COCV 1 (1996), 35-75. http://www.emath.fr/cocv/.
    • (1996) ESAIM: COCV , vol.1 , pp. 35-75
    • Coron, J.-M.1
  • 29
    • 0030313177 scopus 로고    scopus 로고
    • Global exact controllability of the 2D Navier-Stokes equations on a manifold without boundary
    • J.-M. Coron, A. Fursikov, Global exact controllability of the 2D Navier-Stokes equations on a manifold without boundary. Russian J. Math. Phys. 4(4) (1996), 1-19.
    • (1996) Russian J. Math. Phys. , vol.4 , Issue.4 , pp. 1-19
    • Coron, J.-M.1    Fursikov, A.2
  • 30
    • 0000673777 scopus 로고
    • On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity
    • C. Dafermos, On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity. Arch. Rat. Mech. Anal. 29 (1968), 241-271.
    • (1968) Arch. Rat. Mech. Anal. , vol.29 , pp. 241-271
    • Dafermos, C.1
  • 33
    • 84996142009 scopus 로고    scopus 로고
    • Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems
    • C. Fabre, Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems. ESAIM: COCV 1 (1996), 267-302. http://www.emath.fr/cocv/.
    • (1996) ESAIM: COCV , vol.1 , pp. 267-302
    • Fabre, C.1
  • 34
    • 84971109212 scopus 로고
    • Approximate controllability of the semilinear heat equation
    • C. Fabre, J. P. Puel, E. Zuazua, Approximate controllability of the semilinear heat equation, Proc. Royal Soc., Edinburgh, vol. 125 A, 1995, pp. 31-61.
    • (1995) Proc. Royal Soc., Edinburgh , vol.125 A , pp. 31-61
    • Fabre, C.1    Puel, J.P.2    Zuazua, E.3
  • 37
    • 0016050820 scopus 로고
    • Uniform bounds on biorthogonal functions for real exponentials with an application to the control theory of parabolic equations
    • H. Fattorini, D.L. Russell, Uniform bounds on biorthogonal functions for real exponentials with an application to the control theory of parabolic equations. Quart. Appl. Math. 32 (1974), 45-69.
    • (1974) Quart. Appl. Math. , vol.32 , pp. 45-69
    • Fattorini, H.1    Russell, D.L.2
  • 38
    • 84947513673 scopus 로고
    • Global atractors for semilinear wave equations with locally distributed damping and critical exponent
    • E. Feireisl, E. Zuazua, Global atractors for semilinear wave equations with locally distributed damping and critical exponent. Comm. P. D. E. 18(9&10) (1993), 1539-1556.
    • (1993) Comm. P. D. E. , vol.18 , Issue.9-10 , pp. 1539-1556
    • Feireisl, E.1    Zuazua, E.2
  • 39
    • 0033244571 scopus 로고    scopus 로고
    • Approximate controllability for the semilinear heat equation involving gradient terms
    • L. A. Fernández, E. Zuazua, Approximate controllability for the semilinear heat equation involving gradient terms. J. Optim. Theory Appls. 101(2) (1999), 307-328.
    • (1999) J. Optim. Theory Appls. , vol.101 , Issue.2 , pp. 307-328
    • Fernández, L.A.1    Zuazua, E.2
  • 40
    • 84996139962 scopus 로고    scopus 로고
    • Null controllability of the semilinear heat equation
    • E. Fernández-Cara, Null controllability of the semilinear heat equation. ESAIM: COCV 2 (1997), 87-107. http://www.emath.fr/cocv/.
    • (1997) ESAIM: COCV , vol.2 , pp. 87-107
    • Fernández-Cara, E.1
  • 41
    • 0001433193 scopus 로고    scopus 로고
    • The cost of approximate controllability for heat equations: The linear case
    • E. Fernández-Cara, E. Zuazua, The cost of approximate controllability for heat equations: The linear case. Advances Diff. Eqs. 5(4-6) (2000), 465-514.
    • (2000) Advances Diff. Eqs. , vol.5 , Issue.4-6 , pp. 465-514
    • Fernández-Cara, E.1    Zuazua, E.2
  • 42
    • 0000801027 scopus 로고
    • Exact boundary zero controllability of three dimensional Navier-Stokes equations
    • A. V. Fursikov, Exact boundary zero controllability of three dimensional Navier-Stokes equations. Journal of Dynamical and Control Systems 1(3) (1995), 325-350.
    • (1995) Journal of Dynamical and Control Systems , vol.1 , Issue.3 , pp. 325-350
    • Fursikov, A.V.1
  • 43
    • 0032024209 scopus 로고    scopus 로고
    • Imanuvilov, local exact controllability of the Boussinesqu equation
    • A. V. Fursikov, O. Yu. Imanuvilov, Local exact controllability of the Boussinesqu equation. SIAM J. Cont. Opt. 36(2) (1998), 391-421.
    • (1998) SIAM J. Cont. Opt. , vol.36 , Issue.2 , pp. 391-421
    • Fursikov, A.V.1    Yu, O.2
  • 44
    • 0002581635 scopus 로고
    • Imanuvilov, on exact boundary zero-controllability of two-dimensional Navier-Stokes equations
    • A. V. Fursikov, O. Yu. Imanuvilov, On exact boundary zero-controllability of two-dimensional Navier-Stokes equations. Acta Applicandae Mathematicae 37 (1994), 67-76.
    • (1994) Acta Applicandae Mathematicae , vol.37 , pp. 67-76
    • Fursikov, A.V.1    Yu, O.2
  • 45
    • 0003252621 scopus 로고    scopus 로고
    • Imanuvilov, controllability of evolution equations
    • Research Institute of Mathematics, Global Analysis Research Center, Seoul National University
    • A. V. Fursikov, O. Yu. Imanuvilov, Controllability of evolution equations, Lecture Notes Series # 34, Research Institute of Mathematics, Global Analysis Research Center, Seoul National University, 1996.
    • (1996) Lecture Notes Series # 34 , vol.34
    • Fursikov, A.V.1    Yu, O.2
  • 46
    • 0342670035 scopus 로고
    • Some backward uniqueness results
    • J. M. Ghidaglia, Some backward uniqueness results. Nonlinear Anal. TMA. 10 (1986), 777-790.
    • (1986) Nonlinear Anal. TMA , vol.10 , pp. 777-790
    • Ghidaglia, J.M.1
  • 47
    • 0001342333 scopus 로고
    • Microlocal defect measures
    • P. Gérard, Microlocal defect measures. Comm. P. D. E. 16 (1991), 1761-1794.
    • (1991) Comm. P. D. E. , vol.16 , pp. 1761-1794
    • Gérard, P.1
  • 49
    • 0002717380 scopus 로고
    • Ensuring well-posedness by analogy; Stokes problem and boundary control for the wave equation
    • R. Glowinski, Ensuring well-posedness by analogy; Stokes problem and boundary control for the wave equation. J. Compt. Physics 103(2) (1992), 189-221.
    • (1992) J. Compt. Physics , vol.103 , Issue.2 , pp. 189-221
    • Glowinski, R.1
  • 50
    • 77951512192 scopus 로고
    • A numerical approach to the exact boundary controllability of the wave equation (I). Dirichlet controls: Description of the numerical methods
    • R. Glowinski, C. H. Li, J.-L. Lions, A numerical approach to the exact boundary controllability of the wave equation (I). Dirichlet controls: Description of the numerical methods. Japan J. Appl. Math. 7 (1990), 1-76.
    • (1990) Japan J. Appl. Math. , vol.7 , pp. 1-76
    • Glowinski, R.1    Li, C.H.2    Lions, J.-L.3
  • 51
    • 0000326783 scopus 로고
    • Contrôlabilité exacte des solutions de l'équation des ondes en présence de singularités
    • P. Grisvard, Contrôlabilité exacte des solutions de l'équation des ondes en présence de singularités. J. Math. Pures Appl. 68 (1989), 215-259.
    • (1989) J. Math. Pures Appl. , vol.68 , pp. 215-259
    • Grisvard, P.1
  • 52
    • 0028467682 scopus 로고
    • Boundary control of a one-dimensional, linear, thermoelastic rod
    • S. Hansen, Boundary control of a one-dimensional, linear, thermoelastic rod. SIAM J. Cont. Optim. 32(4) (1994), 1052-1074.
    • (1994) SIAM J. Cont. Optim. , vol.32 , Issue.4 , pp. 1052-1074
    • Hansen, S.1
  • 53
    • 21144456241 scopus 로고
    • On a completion problem in the theory of distributed control of the wave equation
    • Nonlinear Partial Differential Equations and their Applications, College de France Seminar, vol. X, H. Brezis and J.-L. Lions eds.
    • A. Haraux, On a completion problem in the theory of distributed control of the wave equation, Nonlinear Partial Differential Equations and their Applications, College de France Seminar, vol. X, H. Brezis and J.-L. Lions eds., Pitman Research Notes in Mathematics 220 (1991), pp. 241-271.
    • (1991) Pitman Research Notes in Mathematics , vol.220 , pp. 241-271
    • Haraux, A.1
  • 54
    • 0003987325 scopus 로고
    • Quelques propriétés des séries lacunaires utiles dans l'étude des vibrations élastiques
    • Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, vol. XII, Paris, 1991-1993, H. Brezis and J.-L. Lions eds., Longman Sci. Tech., Harlow
    • A. Haraux, Quelques propriétés des séries lacunaires utiles dans l'étude des vibrations élastiques, Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, vol. XII, Paris, 1991-1993, H. Brezis and J.-L. Lions eds., Pitman Research Notes in Mathematics Ser. 302, Longman Sci. Tech., Harlow (1994), pp. 113-124.
    • (1994) Pitman Research Notes in Mathematics Ser. , vol.302 , pp. 113-124
    • Haraux, A.1
  • 55
    • 0000089068 scopus 로고
    • Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire
    • A. Haraux, Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire. J. Math. Pures Appl. 08 (1989), 457-465.
    • (1989) J. Math. Pures Appl. , vol.8 , pp. 457-465
    • Haraux, A.1
  • 56
    • 0000066849 scopus 로고
    • Decay estimates for some semilinear damped hyperbolic problems
    • A. Haraux, E. Zuazua, Decay estimates for some semilinear damped hyperbolic problems. Arch. Rational Mech. Anal. 100(2) (1988), 191-206.
    • (1988) Arch. Rational Mech. Anal. , vol.100 , Issue.2 , pp. 191-206
    • Haraux, A.1    Zuazua, E.2
  • 58
    • 0001490384 scopus 로고
    • Observabilité frontière de l'équation des ondes
    • L. F. Ho, Observabilité frontière de l'équation des ondes. C. R. Acad. Sci. Paris 302 (1986), 443-446.
    • (1986) C. R. Acad. Sci. Paris , vol.302 , pp. 443-446
    • Ho, L.F.1
  • 59
    • 25844444415 scopus 로고
    • Vibrating strings with free ends
    • M. Horvath, Vibrating strings with free ends. Acta Math. Hung. 51 (1988), 171-198.
    • (1988) Acta Math. Hung. , vol.51 , pp. 171-198
    • Horvath, M.1
  • 60
    • 0001005992 scopus 로고
    • Boundary controllability of parabolic equations
    • in Russian
    • O. Yu. Imanuvilov, Boundary controllability of parabolic equations. Russian Acad. Sci. Sb. Math. 186 (1995), 109-132 (in Russian).
    • (1995) Russian Acad. Sci. Sb. Math. , vol.186 , pp. 109-132
    • Imanuvilov, O.Yu.1
  • 61
    • 0013242084 scopus 로고    scopus 로고
    • Carleman estimate for a parabolic equation in Sobolev spaces of negative order and its applications
    • G. Chen ct al. eds., Marcel-Dekker
    • O. Yu Imanuvilov, M. Yamamoto, Carleman estimate for a parabolic equation in Sobolev spaces of negative order and its applications, Control of Nonlinear Distributed Parameter Systems, G. Chen ct al. eds., Marcel-Dekker, 2000, pp. 113-137.
    • (2000) Control of Nonlinear Distributed Parameter Systems , pp. 113-137
    • Imanuvilov, O.Yu.1    Yamamoto, M.2
  • 62
    • 0032020274 scopus 로고    scopus 로고
    • Boundary observability for the space-discretizations of the 1 - D wave equation
    • J. A. Infante, E. Zuazua, Boundary observability for the space-discretizations of the 1 - d wave equation. C. R. Acad. Sci. Paris 326 (1998), 713-718.
    • (1998) C. R. Acad. Sci. Paris , vol.326 , pp. 713-718
    • Infante, J.A.1    Zuazua, E.2
  • 63
    • 0033411395 scopus 로고    scopus 로고
    • Boundary observability for the space semi-discretizations of the 1 - D wave equation
    • 2AN 33(2) (1999), 407-438.
    • (1999) 2AN , vol.33 , Issue.2 , pp. 407-438
    • Infante, J.A.1    Zuazua, E.2
  • 66
    • 0040241934 scopus 로고
    • Contrôlabilité exacte et propriétés d'oscillation de l'équation des ondes par analyse nonharmonique
    • I. Joo, Contrôlabilité exacte et propriétés d'oscillation de l'équation des ondes par analyse nonharmonique. C. R. Acad. Sci. Paris 312 (1991), 119-122.
    • (1991) C. R. Acad. Sci. Paris , vol.312 , pp. 119-122
    • Joo, I.1
  • 67
    • 0003309317 scopus 로고
    • Exact controllability and stabilization: The multiplier method
    • Masson & John Wiley
    • V. Komornik, Exact controllability and stabilization: the multiplier method, Masson & John Wiley, RAM 36, 1994.
    • (1994) RAM , vol.36
    • Komornik, V.1
  • 68
    • 0003221008 scopus 로고
    • On moment theory and controllability of one-dimensional vibrating systems and heating processes
    • Springer Verlag
    • W. Krabs, On moment theory and controllability of one-dimensional vibrating systems and heating processes, Lecture Notes in Control and Information Sciences, vol. 173, Springer Verlag, 1992.
    • (1992) Lecture Notes in Control and Information Sciences , vol.173
    • Krabs, W.1
  • 69
    • 0003280914 scopus 로고
    • Boundary stabilization of thin plates
    • Philadelphia
    • J. E. Lagnese, Boundary stabilization of thin plates, SIAM Studies in Appl. Math., Philadelphia, 1989.
    • (1989) SIAM Studies in Appl. Math.
    • Lagnese, J.E.1
  • 70
    • 0000881888 scopus 로고
    • Decay of solutions of wave equations in a bounded region with boundary dissipation
    • J. Lagnese, Decay of solutions of wave equations in a bounded region with boundary dissipation. J. Differential Equations 50 (1983), 163-182.
    • (1983) J. Differential Equations , vol.50 , pp. 163-182
    • Lagnese, J.1
  • 73
    • 0000946119 scopus 로고
    • Stabilization of wave and plate-like equations with nonlinear dissipation on the boundary
    • I. Lasiecka, Stabilization of wave and plate-like equations with nonlinear dissipation on the boundary. J. Differential Equations 79 (1989), 340-381.
    • (1989) J. Differential Equations , vol.79 , pp. 340-381
    • Lasiecka, I.1
  • 74
    • 84972506618 scopus 로고
    • Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
    • I. Lasiecka, D. Tataru, Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping. Differential Integral Equations 6 (1993), 507-533.
    • (1993) Differential Integral Equations , vol.6 , pp. 507-533
    • Lasiecka, I.1    Tataru, D.2
  • 75
    • 0002621804 scopus 로고
    • Exact controllability of semilinear abstract systems with applications to waves and plates boundary control
    • I. Lasiecka, R. Triggiani, Exact controllability of semilinear abstract systems with applications to waves and plates boundary control. Appl. Math. & Optim. 23 (1991), 109-154.
    • (1991) Appl. Math. & Optim. , vol.23 , pp. 109-154
    • Lasiecka, I.1    Triggiani, R.2
  • 76
    • 0001207138 scopus 로고
    • 2(∑))-feedback control in the Dirichlet boundary conditions
    • 2(∑))-feedback control in the Dirichlet boundary conditions. J. Diff. Equations 66 (1987), 340-390.
    • (1987) J. Diff. Equations , vol.66 , pp. 340-390
    • Lasiecka, I.1    Triggiani, R.2
  • 77
    • 84974004138 scopus 로고
    • Contrôle analytique I: Estimations a priori
    • G. Lebeau, Contrôle analytique I: Estimations a priori. Duke Math. J. 68(1) (1992), 1-30.
    • (1992) Duke Math. J. , vol.68 , Issue.1 , pp. 1-30
    • Lebeau, G.1
  • 78
    • 85039379740 scopus 로고    scopus 로고
    • Contrôle for distributed systems: The microlocal approach, Current trends in applied mathematics
    • M. A. Herrero and E. Zuazua eds., Madrid
    • G. Lebeau, Contrôle for distributed systems: The microlocal approach, Current trends in applied mathematics, M. A. Herrero and E. Zuazua eds., Editorial Complutense, Madrid, 1996, pp. 181-218.
    • (1996) Editorial Complutense , pp. 181-218
    • Lebeau, G.1
  • 79
    • 0000977450 scopus 로고
    • Contrôle de l'équation de Schrödinger
    • G. Lebeau, Contrôle de l'équation de Schrödinger. J. Math. Pures Appl. 71 (1992), 267-291.
    • (1992) J. Math. Pures Appl. , vol.71 , pp. 267-291
    • Lebeau, G.1
  • 80
    • 0034425469 scopus 로고    scopus 로고
    • The wave equation with oscillatory density: Observability at low density
    • G. Lebeau, The wave equation with oscillatory density: Observability at low density. ESAIM: COCV 5 (2000), 219-258.
    • (2000) ESAIM: COCV , vol.5 , pp. 219-258
    • Lebeau, G.1
  • 81
    • 84963255809 scopus 로고
    • Contrôle exact de l'équation de la chaleur
    • G. Lebeau, L. Robbiano, Contrôle exact de l'équation de la chaleur. Comm. P.D.E. 20 (1995), 335-356.
    • (1995) Comm. P.D.E. , vol.20 , pp. 335-356
    • Lebeau, G.1    Robbiano, L.2
  • 82
    • 0039413486 scopus 로고    scopus 로고
    • Null controllability of a system of linear thermoelasticity
    • G. Lebeau, E. Zuazua, Null controllability of a system of linear thermoelasticity. Archive Rat. Mech. Anal. 141(4) (1998), 297-329.
    • (1998) Archive Rat. Mech. Anal. , vol.141 , Issue.4 , pp. 297-329
    • Lebeau, G.1    Zuazua, E.2
  • 85
    • 25844472954 scopus 로고    scopus 로고
    • Approximate controllability in noncylindrical domain
    • J. Límaco Ferrel, L.A. Medeiros, Approximate controllability in noncylindrical domain. Communications in Applied Analysis 6(3) (2002), 375-392.
    • (2002) Communications in Applied Analysis , vol.6 , Issue.3 , pp. 375-392
    • Ferrel, J.L.1    Medeiros, L.A.2
  • 86
    • 0000210525 scopus 로고
    • Null boundary controllability for semilinear heat equations
    • Y.-J. Lin Guo, W. Littman, Null boundary controllability for semilinear heat equations. Appl. Math. Optim. 32 (1995), 281-316.
    • (1995) Appl. Math. Optim. , vol.32 , pp. 281-316
    • Guo, Y.-J.L.1    Littman, W.2
  • 87
    • 0023966723 scopus 로고
    • Exact controllability, stabilizability and perturbations for distributed systems
    • J.-L. Lions, Exact controllability, stabilizability and perturbations for distributed systems. SIAM Rev. 30 (1988), 1-68.
    • (1988) SIAM Rev. , vol.30 , pp. 1-68
    • Lions, J.-L.1
  • 89
    • 51249161498 scopus 로고
    • Remarks on approximate controllability
    • J.-L. Lions, Remarks on approximate controllability. J. Analyse Math. 59 (1992), 103-116.
    • (1992) J. Analyse Math. , vol.59 , pp. 103-116
    • Lions, J.-L.1
  • 90
    • 0010920998 scopus 로고
    • Are there connections between turbulence and controllability?
    • Analyse ct optimisation de systèmes, Springer-Verlag
    • J.-L. Lions, Are there connections between turbulence and controllability?, Analyse ct optimisation de systèmes, Lecture Notes in Control and Information Sciences #144, Springer-Verlag, 1990.
    • (1990) Lecture Notes in Control and Information Sciences #144 , vol.144
    • Lions, J.-L.1
  • 91
    • 0003016546 scopus 로고
    • Jornadas Hispano-Francesas sobre Control de Sistemas Distribuidos, University of Málaga, Spain
    • J.L. Lions, Remarques sur la contrôlabilité approchée, Jornadas Hispano-Francesas sobre Control de Sistemas Distribuidos, University of Málaga, Spain, 1991, pp. 77-87.
    • (1991) Remarques sur la Contrôlabilité Approchée , pp. 77-87
    • Lions, J.L.1
  • 92
    • 0001215833 scopus 로고
    • Sur l'unicité rétrograde dans les problèmes mixtes paraboliques
    • J.-L. Lions, B. Malgrange, Sur l'unicité rétrograde dans les problèmes mixtes paraboliques. Math. Scan. 8 (1960), 277-286.
    • (1960) Math. Scan. , vol.8 , pp. 277-286
    • Lions, J.-L.1    Malgrange, B.2
  • 93
    • 84996143961 scopus 로고    scopus 로고
    • A generic uniqueness result for the Stokes system and its control theoretical consequences
    • Partial Differential Equations and Applications, P. Marcellini, G. Talenti and E. Visentini eds., Marcel Dekker Inc.
    • J.-L. Lions, E. Zuazua, A generic uniqueness result for the Stokes system and its control theoretical consequences, Partial Differential Equations and Applications, P. Marcellini, G. Talenti and E. Visentini eds., Marcel Dekker Inc., LNPAS vol. 177, 1996, pp. 221-235.
    • (1996) LNPAS , vol.177 , pp. 221-235
    • Lions, J.-L.1    Zuazua, E.2
  • 94
    • 0347742886 scopus 로고    scopus 로고
    • The cost of controlling unstable systems: Time irreversible systems
    • J.-L. Lions, E. Zuazua, The cost of controlling unstable systems: Time irreversible systems. Revista Mat. Univ. Complutense de Madrid 10(2) (1997), 481-523.
    • (1997) Revista Mat. Univ. Complutense de Madrid , vol.10 , Issue.2 , pp. 481-523
    • Lions, J.-L.1    Zuazua, E.2
  • 95
    • 0031454999 scopus 로고    scopus 로고
    • On the cost of controlling unstable systems: The case of boundary controls
    • J.-L. Lions, E. Zuazua, On the cost of controlling unstable systems: The case of boundary controls. J. Anal. Math. LXXIII (1997), 225-249.
    • (1997) J. Anal. Math. , vol.73 , pp. 225-249
    • Lions, J.-L.1    Zuazua, E.2
  • 96
    • 0031138825 scopus 로고    scopus 로고
    • Contrôlabilité exacte des approximations de Galerkin des équations de Navier-Stokes
    • J.-L. Lions, E. Zuazua, Contrôlabilité exacte des approximations de Galerkin des équations de Navier-Stokes. C. R. Acad. Sci. Paris 234 (1997), 1015-1021.
    • (1997) C. R. Acad. Sci. Paris , vol.234 , pp. 1015-1021
    • Lions, J.-L.1    Zuazua, E.2
  • 98
    • 21244456284 scopus 로고    scopus 로고
    • Exact boundary controllability of Galerkin's approximations of Navier-Stokes equations
    • J.-L. Lions, E. Zuazua, Exact boundary controllability of Galerkin's approximations of Navier-Stokes equations. Annali. Scuola Norm. Sup. Pisa XXVI (1998), 605-621.
    • (1998) Annali. Scuola Norm. Sup. Pisa , vol.26 , pp. 605-621
    • Lions, J.-L.1    Zuazua, E.2
  • 99
    • 84996140876 scopus 로고    scopus 로고
    • Partial exact controllability and exponential stability of the higher-dimensional linear thermoelasticity
    • W. J. Liu, Partial exact controllability and exponential stability of the higher-dimensional linear thermoelasticity. ESAIM: COCV 3(1998), 23-48. http://www.enath.fr/cocv/.
    • (1998) ESAIM: COCV , vol.3 , pp. 23-48
    • Liu, W.J.1
  • 100
    • 0032042586 scopus 로고    scopus 로고
    • The exponential stabilization of the higher-dimensional linear thermoviscoelasticity
    • W. J. Liu, The exponential stabilization of the higher-dimensional linear thermoviscoelasticity. J. Math. Pures Appl. 77 (1998), 355-386.
    • (1998) J. Math. Pures Appl. , vol.77 , pp. 355-386
    • Liu, W.J.1
  • 101
    • 0002649786 scopus 로고    scopus 로고
    • Decay rates for dissipative wave equations
    • W. J. Liu, E. Zuazua, Decay rates for dissipative wave equations. Ricerche di Matematica XLVIII (1999), 61-75.
    • (1999) Ricerche di Matematica , vol.48 , pp. 61-75
    • Liu, W.J.1    Zuazua, E.2
  • 102
    • 0035367299 scopus 로고    scopus 로고
    • Uniform stabilization of the higher dimensional system of thermoelasticity with a nonlinear boundary feedback
    • W. J. Liu, E. Zuazua, Uniform stabilization of the higher dimensional system of thermoelasticity with a nonlinear boundary feedback. Quarterly Appl. Math., 59(2) (2001), 269-314.
    • (2001) Quarterly Appl. Math. , vol.59 , Issue.2 , pp. 269-314
    • Liu, W.J.1    Zuazua, E.2
  • 104
    • 0347136869 scopus 로고    scopus 로고
    • Some new results related to the null-controllability of the 1 - D heat equation
    • Ecole Polytechnique, Paris
    • A. López, E. Zuazua, Some new results related to the null-controllability of the 1 - d heat equation, Séminaire Equations aux Dérivées Partielles, Ecole Polytechnique, Paris, 1997-1998.
    • (1997) Séminaire Equations aux Dérivées Partielles
    • López, A.1    Zuazua, E.2
  • 105
    • 0032042041 scopus 로고    scopus 로고
    • Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating coefficients
    • A. López, E. Zuazua, Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating coefficients. C. R. Acad. Sci. Paris 326 (1998), 955-960.
    • (1998) C. R. Acad. Sci. Paris , vol.326 , pp. 955-960
    • López, A.1    Zuazua, E.2
  • 106
    • 0037575409 scopus 로고    scopus 로고
    • A new method to obtain decay rate estimates for dissipative systems with localized damping
    • P. Martinez, A new method to obtain decay rate estimates for dissipative systems with localized damping. Rev. Mat. Complut. 12(1) (1999), 251-283.
    • (1999) Rev. Mat. Complut. , vol.12 , Issue.1 , pp. 251-283
    • Martinez, P.1
  • 107
    • 85039377539 scopus 로고    scopus 로고
    • Uniform boundary controllability of a semi-discrete 1-d wave equation
    • to appear
    • S. Micu, Uniform boundary controllability of a semi-discrete 1-d wave equation. Numerische Mathematik, to appear.
    • Numerische Mathematik
    • Micu, S.1
  • 108
    • 0031235389 scopus 로고    scopus 로고
    • Boundary controllability of a linear hybrid system arising in the control of noise
    • S. Micu, E. Zuazua, Boundary controllability of a linear hybrid system arising in the control of noise. SIAM J. Cont. Optim. 35(5) (1997), 1614-1638.
    • (1997) SIAM J. Cont. Optim. , vol.35 , Issue.5 , pp. 1614-1638
    • Micu, S.1    Zuazua, E.2
  • 109
    • 0032382211 scopus 로고    scopus 로고
    • Asymptotics for the spectrum of a fluid/structure hybrid system arising in the control of noise
    • S. Micu, E. Zuazua, Asymptotics for the spectrum of a fluid/structure hybrid system arising in the control of noise. SIAM J. Math. Anal. 29(4) (1998), 967-1001.
    • (1998) SIAM J. Math. Anal. , vol.29 , Issue.4 , pp. 967-1001
    • Micu, S.1    Zuazua, E.2
  • 110
    • 23044525306 scopus 로고    scopus 로고
    • On the lack of null controllability of the heat equation on the half line
    • S. Micu, E. Zuazua, On the lack of null controllability of the heat equation on the half line. Transactions of the A.M.S. 353(4) (2001), 1635-1659.
    • (2001) Transactions of the A.M.S. , vol.353 , Issue.4 , pp. 1635-1659
    • Micu, S.1    Zuazua, E.2
  • 111
    • 0007222158 scopus 로고    scopus 로고
    • On the lack of null controllability of the heat equation on the half space
    • S. Micu, E. Zuazua, On the lack of null controllability of the heat equation on the half space. Portugaliae Mathematica 58(1) (2001), 1-24.
    • (2001) Portugaliae Mathematica , vol.58 , Issue.1 , pp. 1-24
    • Micu, S.1    Zuazua, E.2
  • 112
    • 0009108711 scopus 로고
    • HUM and the wave equation with variable coefficients
    • M. Milla Miranda, HUM and the wave equation with variable coefficients. Asymptotic Analysis 11 (1995), 317-341.
    • (1995) Asymptotic Analysis , vol.11 , pp. 317-341
    • Miranda, M.M.1
  • 113
    • 1842716441 scopus 로고
    • Notes on time decay and scatterig for some hyperbolic problems
    • SIAM, Philadelphia
    • C. Morawetz, Notes on time decay and scatterig for some hyperbolic problems, Regional Conference Series in Applied Mathematics, vol. 19, SIAM, Philadelphia, 1975.
    • (1975) Regional Conference Series in Applied Mathematics , vol.19
    • Morawetz, C.1
  • 114
    • 0000907825 scopus 로고
    • Asymptotic stability of the bounded or almost periodic solution of the wave equation with a nonlinear dissipative term
    • M. Nakao, Asymptotic stability of the bounded or almost periodic solution of the wave equation with a nonlinear dissipative term, J. Math. Anal. Appl. 58 (1977), 336-343.
    • (1977) J. Math. Anal. Appl. , vol.58 , pp. 336-343
    • Nakao, M.1
  • 115
    • 84972525392 scopus 로고
    • Energy decay for the wave equation with a nonlinear weak dissipation
    • M. Nakao, Energy decay for the wave equation with a nonlinear weak dissipation. Differential Integral Equations 8(3) (1995), 681-188.
    • (1995) Differential Integral Equations , vol.8 , Issue.3 , pp. 681-1188
    • Nakao, M.1
  • 116
    • 0026158019 scopus 로고
    • Invariance of the approximately reachable set under nonlinear perturbations
    • K. Naito, T. Seidman, Invariance of the approximately reachable set under nonlinear perturbations. SIAM J. Cont. Optim. 29(3) (1991), 731-750.
    • (1991) SIAM J. Cont. Optim. , vol.29 , Issue.3 , pp. 731-750
    • Naito, K.1    Seidman, T.2
  • 119
    • 0032066391 scopus 로고    scopus 로고
    • Une nouvelle famille de multiplicateurs et ses applications à la contrôlabilité exacte des ondes
    • A. Osses, Une nouvelle famille de multiplicateurs et ses applications à la contrôlabilité exacte des ondes. C. R. Acad. Sci. Paris 326 (1998), 1099-1104.
    • (1998) C. R. Acad. Sci. Paris , vol.326 , pp. 1099-1104
    • Osses, A.1
  • 120
    • 0042735613 scopus 로고    scopus 로고
    • On the controllability of the Laplace equation observed on an interior curve
    • A. Osses, J. P. Puel, On the controllability of the Laplace equation observed on an interior curve. Rev. Matemática Complutense 11(2) (1998), 403-441.
    • (1998) Rev. Matemática Complutense , vol.11 , Issue.2 , pp. 403-441
    • Osses, A.1    Puel, J.P.2
  • 121
    • 0032345445 scopus 로고    scopus 로고
    • On the controllability of the statonary Stokes system with linear convection observed on an interior curve
    • A. Osses, J. P. Puel, On the controllability of the statonary Stokes system with linear convection observed on an interior curve. Journal of Optimization Theory and Applications 99(1) (1998), 201-234.
    • (1998) Journal of Optimization Theory and Applications , vol.99 , Issue.1 , pp. 201-234
    • Osses, A.1    Puel, J.P.2
  • 122
    • 0004564080 scopus 로고    scopus 로고
    • Energy decay of magnetoelastic waves in a bounded conductive medium
    • G. Perla-Menzala, E. Zuazua, Energy decay of magnetoelastic waves in a bounded conductive medium. Asymptotic Analysis 18 (1998), 349-362.
    • (1998) Asymptotic Analysis , vol.18 , pp. 349-362
    • Perla-Menzala, G.1    Zuazua, E.2
  • 123
    • 84972072973 scopus 로고
    • Exact controllability for a model of a multidimensional flexible structure
    • J. P. Puel, E. Zuazua, Exact controllability for a model of a multidimensional flexible structure, Proc. Roy. Soc. Edinburgh, vol. 123A, 1993, pp. 323-344.
    • (1993) Proc. Roy. Soc. Edinburgh , vol.123 A , pp. 323-344
    • Puel, J.P.1    Zuazua, E.2
  • 124
    • 0016082307 scopus 로고
    • Exponential decay of solutions to symmetric hyperbolic equations in bounded domains
    • J. Rauch, M. Taylor, Exponential decay of solutions to symmetric hyperbolic equations in bounded domains. Indiana J. Math. 24 (1974), 79-86.
    • (1974) Indiana J. Math. , vol.24 , pp. 79-86
    • Rauch, J.1    Taylor, M.2
  • 125
    • 84981752412 scopus 로고
    • Solution of the wave equation with localized energy
    • J. Ralston, Solution of the wave equation with localized energy. Comm. Pure Appl. Math. 22 (1969), 807-823.
    • (1969) Comm. Pure Appl. Math. , vol.22 , pp. 807-823
    • Ralston, J.1
  • 126
    • 0000952462 scopus 로고
    • Gaussian beams and the propagation of singularities
    • Studies in Partial Differential Equations, W. Littman ed.
    • J. Ralston, Gaussian beams and the propagation of singularities, Studies in Partial Differential Equations, MAA Studies in Mathematics, vol. 23, W. Littman ed., 1982, pp. 206-248.
    • (1982) MAA Studies in Mathematics , vol.23 , pp. 206-248
    • Ralston, J.1
  • 127
    • 0039657363 scopus 로고    scopus 로고
    • Uniqueness in the Cauchy problem for operators with partially holomorphic coefficients
    • L. Robbiano, C. Zuily, Uniqueness in the Cauchy problem for operators with partially holomorphic coefficients. Invent. Math. 131 (1998), 493-539.
    • (1998) Invent. Math. , vol.131 , pp. 493-539
    • Robbiano, L.1    Zuily, C.2
  • 128
    • 0000687761 scopus 로고
    • Unique continuation for weak solutions of the wave equation plus a potential
    • A. Ruíz, Unique continuation for weak solutions of the wave equation plus a potential. J. Math. Pures Appl. 71(5) (1992), 455-467.
    • (1992) J. Math. Pures Appl. , vol.71 , Issue.5 , pp. 455-467
    • Ruíz, A.1
  • 129
    • 0000820706 scopus 로고
    • Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions
    • D. L. Russell, Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions. SIAM Rev. 20 (1978), 639-739.
    • (1978) SIAM Rev. , vol.20 , pp. 639-739
    • Russell, D.L.1
  • 130
    • 84961355905 scopus 로고
    • A unified boundary controllability theory for hyperbolic and parabolic partial differential equations
    • D. L. Russell, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations. Studies in Appl. Math. 52 (1973), 189-221.
    • (1973) Studies in Appl. Math. , vol.52 , pp. 189-221
    • Russell, D.L.1
  • 131
    • 0027874593 scopus 로고
    • First-order corrections to the homogenized eigenvalues of a periodic composite medium
    • F. Santosa, M. Vogelius, First-order corrections to the homogenized eigenvalues of a periodic composite medium. SIAM J. Appl. Math. 53 (1993), 1636-1668.
    • (1993) SIAM J. Appl. Math. , vol.53 , pp. 1636-1668
    • Santosa, F.1    Vogelius, M.2
  • 132
    • 0000523343 scopus 로고
    • Unique continuation for some evolution equations
    • J. C. Saut, B. Scheurer, Unique continuation for some evolution equations. J. Diff. Equations 66(1) (1987), 118-139.
    • (1987) J. Diff. Equations , vol.66 , Issue.1 , pp. 118-139
    • Saut, J.C.1    Scheurer, B.2
  • 133
    • 0000983021 scopus 로고
    • A priori estimates of Carleman's type in domains with boundary
    • D. Tataru, A priori estimates of Carleman's type in domains with boundary. J. Math. Pures Appl. 73 (1994), 355-387.
    • (1994) J. Math. Pures Appl. , vol.73 , pp. 355-387
    • Tataru, D.1
  • 134
    • 84957249045 scopus 로고    scopus 로고
    • Unique continuation for solutions to PDE's: Between Hörmander's theorem and Holmgren's theorem
    • D. Tataru, Unique continuation for solutions to PDE's: between Hörmander's theorem and Holmgren's theorem. Comm. PDE 20(0-7) (1996), 855-884.
    • (1996) Comm. PDE , vol.20 , Issue.7 , pp. 855-884
    • Tataru, D.1
  • 136
    • 0000259163 scopus 로고    scopus 로고
    • Controllability of the linear system of thermoelastic plates
    • L. do Teresa, E. Zuazua, Controllability of the linear system of thermoelastic plates. Advances Diff. Equations 1(3) (1996), 369-402.
    • (1996) Advances Diff. Equations , vol.1 , Issue.3 , pp. 369-402
    • Do Teresa, L.1    Zuazua, E.2
  • 137
    • 0033197209 scopus 로고    scopus 로고
    • Approximate controllability of the heat equation in unbounded domains
    • L. de Teresa, E. Zuazua, Approximate controllability of the heat equation in unbounded domains. Nonlinear Anal., T. M. A. 37(8) (1999), 1059-1090.
    • (1999) Nonlinear Anal., T. M. A. , vol.37 , Issue.8 , pp. 1059-1090
    • De Teresa, L.1    Zuazua, E.2
  • 138
    • 0039175425 scopus 로고
    • Contrôle d'une poutre avec actionneur piézoélectrique
    • M. Tucsnak, Contrôle d'une poutre avec actionneur piézoélectrique. C. R. Acad. Sci. Paris 319 (1994), 697-702
    • (1994) C. R. Acad. Sci. Paris , vol.319 , pp. 697-702
    • Tucsnak, M.1
  • 139
    • 0004075348 scopus 로고    scopus 로고
    • On the pointwise stabilization of astring
    • Control and Estimation of Distributed Parameter Systems, W. Desch, F. Kappel and K. Kunisch eds., Birkhäuser Basel
    • M. Tucsnak, On the pointwise stabilization of astring, Control and Estimation of Distributed Parameter Systems, W. Desch, F. Kappel and K. Kunisch eds., Birkhäuser Basel, 1996, International Series of Numerical Mathemtics, vol. 126, pp. 287-296.
    • (1996) International Series of Numerical Mathemtics , vol.126 , pp. 287-296
    • Tucsnak, M.1
  • 140
    • 84966260633 scopus 로고
    • Divided differences and systems of nonharmonic Fourier series
    • D. Ulrich, Divided differences and systems of nonharmonic Fourier series, Proc. A.M.S., vol. 80, 1980, pp. 47-57.
    • (1980) Proc. A.M.S. , vol.80 , pp. 47-57
    • Ulrich, D.1
  • 141
    • 0001489944 scopus 로고
    • Generic properties of eigenfunctions
    • K. Uhlenbeck, Generic properties of eigenfunctions. American J. Math. 98(4) (1976), 1059-1078.
    • (1976) American J. Math. , vol.98 , Issue.4 , pp. 1059-1078
    • Uhlenbeck, K.1
  • 144
    • 0000976025 scopus 로고
    • Exponential decay for semilinear wave equations with localized damping
    • E. Zuazua, Exponential decay for semilinear wave equations with localized damping. Comm. P.D.E. 15(2) (1990), 205-235.
    • (1990) Comm. P.D.E. , vol.15 , Issue.2 , pp. 205-235
    • Zuazua, E.1
  • 145
    • 0003226678 scopus 로고
    • Controllability of the linear system of thermoelasticity
    • E. Zuazua, Controllability of the linear system of thermoelasticity. J. Math. Pures Appl. 74 (1995), 303-346.
    • (1995) J. Math. Pures Appl. , vol.74 , pp. 303-346
    • Zuazua, E.1
  • 146
    • 0003138438 scopus 로고
    • Exact controllability for the semilinear wave equation
    • E. Zuazua, Exact controllability for the semilinear wave equation. J. Math. Pures Appl. 69(1) (1990), 33-55.
    • (1990) J. Math. Pures Appl. , vol.69 , Issue.1 , pp. 33-55
    • Zuazua, E.1
  • 147
    • 0000394374 scopus 로고
    • Exact boundary controllability for the semilinear wave equation
    • H. Brezis and J.-L. Lions eds., Pitman
    • E. Zuazua, Exact boundary controllability for the semilinear wave equation, Nonlinear Partial Differential Equations and their Applications, vol. X, H. Brezis and J.-L. Lions eds., Pitman, 1991, pp. 357-391.
    • (1991) Nonlinear Partial Differential Equations and Their Applications , vol.10 , pp. 357-391
    • Zuazua, E.1
  • 148
    • 85012981810 scopus 로고
    • Exact controllability for semilinear wave equations
    • E. Zuazua, Exact controllability for semilinear wave equations. Ann. Inst. Henri Poincaré 10(1) (1993), 109-129.
    • (1993) Ann. Inst. Henri Poincaré , vol.10 , Issue.1 , pp. 109-129
    • Zuazua, E.1
  • 149
    • 0031091761 scopus 로고    scopus 로고
    • Finite dimensional null controllability for the semilinear heat equation
    • E. Zuazua, Finite dimensional null controllability for the semilinear heat equation. J. Math. Pures Appl. 76 (1997), 570-594.
    • (1997) J. Math. Pures Appl. , vol.76 , pp. 570-594
    • Zuazua, E.1
  • 150
    • 0011244705 scopus 로고
    • An introduction to the exact controllability for distributed systems
    • Ccntro de Matematica e Aplicacoes Fundamentals de la Universidad de Lisboa
    • E. Zuazua, An introduction to the exact controllability for distributed systems. Ccntro de Matematica e Aplicacoes Fundamentals de la Universidad de Lisboa, Textos e Notas # 44, 1990.
    • (1990) Textos e Notas # 44 , vol.44
    • Zuazua, E.1
  • 151
    • 0002915122 scopus 로고    scopus 로고
    • Approximate controllability of the semilinear heat equation: Boundary control
    • M.O. Bristeau et al. eds, John Wiley & Sons
    • E. Zuazua, Approximate controllability of the semilinear heat equation: boundary control, Computational Science for the 21st Century, M.O. Bristeau et al. eds, John Wiley & Sons, 1997, pp. 738-747.
    • (1997) Computational Science for the 21st Century , pp. 738-747
    • Zuazua, E.1
  • 153
    • 0008732910 scopus 로고    scopus 로고
    • Some problems and results on the controllability of partial differential equations
    • Proc. of the Second European Conference of Mathematics, Budapest, July 1996, Birkhäuser Verlag Basel/Switzerland
    • E. Zuazua, Some problems and results on the controllability of partial differential equations, Proc. of the Second European Conference of Mathematics, Budapest, July 1996, Progress in Mathematics, vol. 169, 1998, Birkhäuser Verlag Basel/Switzerland, pp. 276-311.
    • (1998) Progress in Mathematics , vol.169 , pp. 276-311
    • Zuazua, E.1
  • 154
    • 84974742898 scopus 로고
    • Stability and decay for a class of nonlinear hyperbolic problems
    • E. Zuazua, Stability and decay for a class of nonlinear hyperbolic problems. Asymptotic Analysis 1(2) (1988), 1-28.
    • (1988) Asymptotic Analysis , vol.1 , Issue.2 , pp. 1-28
    • Zuazua, E.1
  • 155
    • 0025401475 scopus 로고
    • Uniform stabilization of the wave equation by nonlinear boundary feedback
    • E. Zuazua, Uniform stabilization of the wave equation by nonlinear boundary feedback. SIAM J. Control Optim. 28(2) (1990), 466-477.
    • (1990) SIAM J. Control Optim. , vol.28 , Issue.2 , pp. 466-477
    • Zuazua, E.1
  • 156
    • 0033542257 scopus 로고    scopus 로고
    • Boundary observability for the finite-difference space semi-discretizations of the 2 - D wave equation in the square
    • E. Zuazua, Boundary observability for the finite-difference space semi-discretizations of the 2 - d wave equation in the square. J. Math. Pures Appl. 78 (1999), 523-563.
    • (1999) J. Math. Pures Appl. , vol.78 , pp. 523-563
    • Zuazua, E.1
  • 157
    • 0033265731 scopus 로고    scopus 로고
    • Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities
    • E. Zuazua, Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities. Control and Cybernetics 28(3) (1999), 665-683.
    • (1999) Control and Cybernetics , vol.28 , Issue.3 , pp. 665-683
    • Zuazua, E.1
  • 158
    • 0043236862 scopus 로고    scopus 로고
    • Observability of 1 - D waves in heterogeneous and semi-discrete media
    • J. Rodellar ct al. eds, CIMNE, Barcelona
    • E. Zuazua, Observability of 1 - d waves in heterogeneous and semi-discrete media, Advances in Structural Control, J. Rodellar ct al. eds, CIMNE, Barcelona, 1999, pp. 1-30.
    • (1999) Advances in Structural Control , pp. 1-30
    • Zuazua, E.1


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