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Volumn 37, Issue 2, 1998, Pages 543-565

Exact boundary controllability of the Korteweg-de Vries equation

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEM ANALYSIS; DISTRIBUTED PARAMETER CONTROL SYSTEMS;

EID: 0032201986     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0363012997327501     Document Type: Article
Times cited : (89)

References (33)
  • 1
    • 0016369301 scopus 로고
    • The inverse scattering transform - Fourier analysis for nonlinear problems
    • M. J. ABLOWITZ, D. J. KAUP, A. C. NEWELL, AND H. SEGUR, The inverse scattering transform - Fourier analysis for nonlinear problems, Stud. Appl. Math., 53 (1974), pp. 249-315.
    • (1974) Stud. Appl. Math. , vol.53 , pp. 249-315
    • Ablowitz, M.J.1    Kaup, D.J.2    Newell, A.C.3    Segur, H.4
  • 2
    • 0001119719 scopus 로고
    • The initial value problem for the Korteweg-de Vries equation
    • J. L. BONA AND R. SMITH, The initial value problem for the Korteweg-de Vries equation, Philos. Trans. Roy. Soc. London Ser. A, 278 (1975), pp. 555-601.
    • (1975) Philos. Trans. Roy. Soc. London Ser. A , vol.278 , pp. 555-601
    • Bona, J.L.1    Smith, R.2
  • 3
    • 21344442079 scopus 로고    scopus 로고
    • The initial-value problem for the forced Korteweg-de Vries equation
    • J. L. BONA AND B.-Y. ZHANG, The initial-value problem for the forced Korteweg-de Vries equation, Proc. Roy. Soc. Edinburgh Ser. A. 126 (1996), pp. 571-598.
    • (1996) Proc. Roy. Soc. Edinburgh Ser. A. , vol.126 , pp. 571-598
    • Bona, J.L.1    Zhang, B.-Y.2
  • 4
    • 34250084341 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and applications to non-linear evolution equations, part I: Schrödinger equations
    • J. BOURGAIN, Fourier transform restriction phenomena for certain lattice subsets and applications to non-linear evolution equations, part I: Schrödinger equations, Geom. Funct. Anal., 3 (1993), pp. 107-156.
    • (1993) Geom. Funct. Anal. , vol.3 , pp. 107-156
    • Bourgain, J.1
  • 5
    • 0009303159 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and applications to non-linear evolution equations, part II: The KdV equation
    • J. BOURGAIN, Fourier transform restriction phenomena for certain lattice subsets and applications to non-linear evolution equations, part II: The KdV equation, Geom. Funct. Anal., 3 (1993), pp. 209-262.
    • (1993) Geom. Funct. Anal. , vol.3 , pp. 209-262
    • Bourgain, J.1
  • 6
    • 84972563462 scopus 로고
    • Solutions of the Korteweg-de Vries equation from irregular data
    • A. COHEN, Solutions of the Korteweg-de Vries equation from irregular data, Duke Math. J., 45 (1978), pp. 149-181.
    • (1978) Duke Math. J. , vol.45 , pp. 149-181
    • Cohen, A.1
  • 7
    • 84968508844 scopus 로고
    • Local smoothing properties of dispersive equations
    • P. CONSTANTIN AND J.-C. SAUT, Local smoothing properties of dispersive equations, J. Amer. Math. Soc., 1 (1988), pp. 413-446.
    • (1988) J. Amer. Math. Soc. , vol.1 , pp. 413-446
    • Constantin, P.1    Saut, J.-C.2
  • 10
    • 0002362136 scopus 로고
    • On the cauchy problem for the (generalized) Korteweg-de Vries equations
    • Academic Press, New York
    • T. KATO, On the Cauchy problem for the (generalized) Korteweg-de Vries equations, in Advances in Mathematics Supplementary Studies, Stud. Appl. Math. 8, Academic Press, New York, 1983, pp. 93-128.
    • (1983) Advances in Mathematics Supplementary Studies, Stud. Appl. Math. , vol.8 , pp. 93-128
    • Kato, T.1
  • 11
    • 84968502715 scopus 로고
    • Well-posedness of the initial value problem for the KdV equation
    • C. E. KENIG, G. PONCE, AND L. VEGA, Well-posedness of the initial value problem for the KdV equation, J. Amer. Math. Soc., 4 (1991), pp. 323-347.
    • (1991) J. Amer. Math. Soc. , vol.4 , pp. 323-347
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 12
    • 84990553608 scopus 로고
    • Well-posedness and scattering results for the generalized Korteweg-de Vries equations via the contraction principle
    • C. E. KENIG, G. PONCE, AND L. VEGA, Well-posedness and scattering results for the generalized Korteweg-de Vries equations via the contraction principle, Comm. Pure Appl. Math., 46 (1993), pp. 527-620.
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 527-620
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 13
    • 84974004169 scopus 로고
    • The cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
    • C. E. KENIG, G. PONCE, AND L. VEGA, The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices, Duke Math. J., 71 (1993), pp. 1-21.
    • (1993) Duke Math. J. , vol.71 , pp. 1-21
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 14
    • 0030528276 scopus 로고    scopus 로고
    • A bilinear estimate with applications to the KdV equation
    • C. E. KENIG, G. PONCE, AND L. VEGA, A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc., 9 (1996), pp. 573-603.
    • (1996) J. Amer. Math. Soc. , vol.9 , pp. 573-603
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 16
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
    • D. J. KORTEWEG AND G. DEVRIES, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag., 39 (1895), pp. 422-443.
    • (1895) Philos. Mag. , vol.39 , pp. 422-443
    • Korteweg, D.J.1    DeVries, G.2
  • 17
    • 0005351956 scopus 로고
    • Boundary control theory for hyperbolic and parabolic partial differential equations with constant coefficients
    • W. LITTMAN, Boundary control theory for hyperbolic and parabolic partial differential equations with constant coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 5 (1978), pp. 567-580.
    • (1978) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.5 , pp. 567-580
    • Littman, W.1
  • 18
    • 51249162638 scopus 로고
    • Smoothing evolution equations and boundary control theory Festschrift on the occasion of the 70th birthday of Shmuel Agmon
    • W. LITTMAN AND S. TAYLOR, Smoothing evolution equations and boundary control theory. Festschrift on the occasion of the 70th birthday of Shmuel Agmon, J. Anal. Math., 59 (1992), pp. 117-131.
    • (1992) J. Anal. Math. , vol.59 , pp. 117-131
    • Littman, W.1    Taylor, S.2
  • 19
    • 0016973738 scopus 로고
    • The Korteweg-de Vries equation: A survey of results
    • R. M. MIURA, The Korteweg-de Vries equation: A survey of results, SIAM Rev., 18 (1976), pp. 412-459.
    • (1976) SIAM Rev. , vol.18 , pp. 412-459
    • Miura, R.M.1
  • 20
    • 0003316678 scopus 로고
    • Semigroup of linear operators and applications to partial differential equations
    • Springer-Verlag, New York
    • A. PAZY, Semigroup of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer-Verlag, New York, 1983.
    • (1983) Appl. Math. Sci. , vol.44
    • Pazy, A.1
  • 21
    • 84996141528 scopus 로고    scopus 로고
    • Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
    • L. ROSIER, Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain, ESIAM Control Optim. Cal. Var., 2 (1997), pp. 33-55.
    • (1997) ESIAM Control Optim. Cal. Var. , vol.2 , pp. 33-55
    • Rosier, L.1
  • 22
    • 0015008050 scopus 로고
    • Boundary value control of the higher-dimensional wave equation
    • D. L. RUSSELL, Boundary value control of the higher-dimensional wave equation, SIAM J. Control Optim., 9 (1971), pp. 29-42.
    • (1971) SIAM J. Control Optim. , vol.9 , pp. 29-42
    • Russell, D.L.1
  • 23
    • 0015112656 scopus 로고
    • Boundary value control theory of the higher-dimensional wave equation part II
    • D. L. RUSSELL, Boundary value control theory of the higher-dimensional wave equation part II. SIAM J. Control Optim., 9 (1971), pp. 401-419.
    • (1971) SIAM J. Control Optim. , vol.9 , pp. 401-419
    • Russell, D.L.1
  • 24
    • 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), pp. 639-739.
    • (1978) SIAM Rev. , vol.20 , pp. 639-739
    • Russell, D.L.1
  • 25
    • 0027594486 scopus 로고
    • Controllability and stabilizability of the third-order linear dispersion equation of a periodic domain
    • D. L. RUSSELL AND B.-Y. ZHANG, Controllability and stabilizability of the third-order linear dispersion equation of a periodic domain, SIAM J. Control Optim., 31 (1993), pp. 659-676.
    • (1993) SIAM J. Control Optim. , vol.31 , pp. 659-676
    • Russell, D.L.1    Zhang, B.-Y.2
  • 26
    • 0000140289 scopus 로고
    • Smoothing and decay properties of solutions of the Korteweg-de Vries equation on a periodic domain with point dissipation
    • D. L. RUSSELL AND B.-Y. ZHANG, Smoothing and decay properties of solutions of the Korteweg-de Vries equation on a periodic domain with point dissipation, J. Math. Anal. Appl., 190 (1995), pp. 449-488.
    • (1995) J. Math. Anal. Appl. , vol.190 , pp. 449-488
    • Russell, D.L.1    Zhang, B.-Y.2
  • 27
    • 21444446596 scopus 로고    scopus 로고
    • Exact controllability and stabilizability of the Korteweg-de Vries equation
    • D. L. RUSSELL AND B.-Y. ZHANG, Exact controllability and stabilizability of the Korteweg-de Vries equation, Trans. Amer. Math. Soc., 348 (1996), pp. 3643-3672.
    • (1996) Trans. Amer. Math. Soc. , vol.348 , pp. 3643-3672
    • Russell, D.L.1    Zhang, B.-Y.2
  • 28
    • 51649183085 scopus 로고
    • Remarks on the Korteweg-de Vries equation
    • J. C. SAUT AND R. TEMAM, Remarks on the Korteweg-de Vries equation, Israel J. Math., 24 (1976), pp. 78-87.
    • (1976) Israel J. Math. , vol.24 , pp. 78-87
    • Saut, J.C.1    Temam, R.2
  • 29
    • 0000600898 scopus 로고
    • Sur un problème non linéaire
    • R. TEMAM, Sur un problème non linéaire, J. Math. Pures Appl., 48 (1969), pp. 159-172.
    • (1969) J. Math. Pures Appl. , vol.48 , pp. 159-172
    • Temam, R.1
  • 30
    • 0005748256 scopus 로고
    • Unique continuation for the Korteweg-De Vries equation
    • B.-Y. ZHANG, Unique continuation for the Korteweg-De Vries equation, SIAM J. Math. Anal., 23 (1992), pp. 55-71.
    • (1992) SIAM J. Math. Anal. , vol.23 , pp. 55-71
    • Zhang, B.-Y.1
  • 31
    • 0005142356 scopus 로고
    • Taylor series expansion for solutions of the Korteweg-de Vries equation with respect to their initial values
    • B.-Y. ZHANG, Taylor series expansion for solutions of the Korteweg-de Vries equation with respect to their initial values, J. Funct. Anal., 129 (1995), pp. 293-324.
    • (1995) J. Funct. Anal. , vol.129 , pp. 293-324
    • Zhang, B.-Y.1
  • 32
    • 0042625574 scopus 로고
    • Analyticity of solutions of the generalized Korteweg-de Vries equations with respect to their initial values
    • B.-Y. ZHANG, Analyticity of solutions of the generalized Korteweg-de Vries equations with respect to their initial values, SIAM J. Math. Anal., 26 (1995), pp. 1488-1513.
    • (1995) SIAM J. Math. Anal. , vol.26 , pp. 1488-1513
    • Zhang, B.-Y.1
  • 33
    • 84972545039 scopus 로고
    • A remark on the Cauchy problem of the periodic Korteweg-de Vries equation
    • B.-Y. ZHANG, A remark on the Cauchy problem of the periodic Korteweg-de Vries equation, Differential Integral Equations, 8 (1995), pp. 1191-1204.
    • (1995) Differential Integral Equations , vol.8 , pp. 1191-1204
    • Zhang, B.-Y.1


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