메뉴 건너뛰기




Volumn 2001, Issue , 2001, Pages

An abstract approximate controllability result and applications to elliptic and parabolic systems with dynamic boundary conditions

Author keywords

Approximate controllability; Dynamic boundary conditions; Elliptic problem; Evolution equation; Parabolic problem

Indexed keywords


EID: 52549089395     PISSN: 10726691     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (22)

References (72)
  • 1
    • 33846815273 scopus 로고
    • On quasilinear parabolic systems
    • P. ACQUISTAPACE, B. TERRENI, On quasilinear parabolic systems, Math. Ann., 281(1988), 315-335.
    • (1988) Math. Ann. , vol.281 , pp. 315-335
    • Acquistapace, P.1    Terreni, B.2
  • 2
    • 34347214755 scopus 로고
    • Multi-dimensional Stefan Problems with Dynamic Boundary Conditions
    • T. AlKI, Multi-dimensional Stefan Problems with Dynamic Boundary Conditions, Applicabl Analysis, 56(1995), 71-94.
    • (1995) Applicabl Analysis , vol.56 , pp. 71-94
    • Alki, T.1
  • 3
    • 52549116419 scopus 로고
    • The prediction of transient heat transfer performanc of thermal energy storage devices
    • M. ALTMAN, D. P. Ross, H. CHANG, The prediction of transient heat transfer performanc of thermal energy storage devices, Chem. Eng. Progress Symposium Ser., 61(1965), 289-297.
    • (1965) Chem. Eng. Progress Symposium Ser. , vol.61 , pp. 289-297
    • Altman, M.1    Ross, D.P.2    Chang, H.3
  • 4
    • 53349128723 scopus 로고    scopus 로고
    • Strongly continuous dual semigroups
    • H. AMANN, J. ESCHER, Strongly continuous dual semigroups, Ann. Mat. Pura et Appl., CLXXI(1996), 41-62.
    • (1996) Ann. Mat. Pura et Appl. , vol.171 , pp. 41-62
    • Amann, H.1    Escher, J.2
  • 5
    • 0039229292 scopus 로고    scopus 로고
    • A Fujita-type theorem for the Laplace equation with a dynamica boundary condition
    • H. AMANN, M. FILA, A Fujita-type theorem for the Laplace equation with a dynamica boundary condition, Acta Math. Univ. Comenianae, 66(1997), 321-328.
    • (1997) Acta Math. Univ. Comenianae , vol.66 , pp. 321-328
    • Amann, H.1    Fila, M.2
  • 8
    • 0000484888 scopus 로고
    • Compacité de l'opérateur définissant la solution d'une équation d'évolution non homogène
    • P. BARAS, J. C. HASSAN, L. VERON, Compacité de l'opérateur définissant la solution d'une équation d'évolution non homogène, C. R. Acad. Sci. Paris Sér. I Math., 284(1977), 779-802.
    • (1977) C. R. Acad. Sci. Paris Sér. i Math. , vol.284 , pp. 779-802
    • Baras, P.1    Hassan, J.C.2    Veron, L.3
  • 9
    • 0015768944 scopus 로고
    • Sur l'unicité rétrograde des équations paraboliques et quelques questions voisines
    • C. BARDOS, L. TARTAR, Sur l'unicité rétrograde des équations paraboliques et quelques questions voisines, Arch. Ration. Mech. Analysis, 50(1973), 10-25.
    • (1973) Arch. Ration. Mech. Analysis , vol.50 , pp. 10-25
    • Bardos, C.1    Tartar, L.2
  • 10
    • 0039355035 scopus 로고
    • Modified Sturm-Liouville systems
    • W. F. BAUER, Modified Sturm-Liouville systems, Quart. Appl. Math., 11(1953), 273-282.
    • (1953) Quart. Appl. Math. , vol.11 , pp. 273-282
    • Bauer, W.F.1
  • 12
    • 52549125836 scopus 로고    scopus 로고
    • Personal communication, unpublished
    • P. BENILAN, Personal communication, unpublished.
    • Benilan, P.1
  • 13
    • 0020292888 scopus 로고
    • Hamiltonian structure, symmetriies and conservation laws for water waves
    • T. BENJAMIN, P. OLVER, Hamiltonian structure, symmetriies and conservation laws for water waves, J. Fluid Mech. 125(1982), 137-185.
    • (1982) J. Fluid Mech. , vol.125 , pp. 137-185
    • Benjamin, T.1    Olver, P.2
  • 15
    • 0001968839 scopus 로고
    • Problèmes Unilatéraux
    • H. BREZIS, Problèmes Unilatéraux, J. Math. Pures et Appl., 51(1972), 1-168.
    • (1972) J. Math. Pures et Appl. , vol.51 , pp. 1-168
    • Brezis, H.1
  • 18
  • 22
    • 0005805992 scopus 로고
    • Parabolic equations with nonlinear time-dependent boundary conditions
    • M. DEGIOVANNI, Parabolic equations with nonlinear time-dependent boundary conditions, Ann. Mat. Pura Appl., 141(1985), 223-263.
    • (1985) Ann. Mat. Pura Appl. , vol.141 , pp. 223-263
    • Degiovanni, M.1
  • 23
    • 52549099080 scopus 로고
    • On the controllability of some simple climate models
    • J. I. DÎAZ, J. L. LlONS Editors, Masson, Paris
    • J. I. DlAZ, On the controllability of some simple climate models. In Environment, Economics and their Mathematical Models, J. I. DÎAZ, J. L. LlONS Editors, Masson, Paris, 1994, 29-44.
    • (1994) Environment, Economics and Their Mathematical Models , pp. 29-44
    • Dlaz, J.I.1
  • 24
    • 0031703704 scopus 로고    scopus 로고
    • On the approximate controllability of some semilinear parabolic boundary-value problems
    • J. I. DlAZ, J. HENRY, A. M. RAMOS, On the approximate controllability of some semilinear parabolic boundary-value problems, Appl. Math. Optim., 37(1998), 71-97.
    • (1998) Appl. Math. Optim. , vol.37 , pp. 71-97
    • Dlaz, J.I.1    Henry, J.2    Ramos, A.M.3
  • 25
    • 52549105224 scopus 로고
    • Aplicaciön de la teoria no lineal de semigrupos a un operador pseudodiferencial
    • J. I. DlAZ, R. JlMENEZ, Aplicaciön de la teoria no lineal de semigrupos a un operador pseudodiferencial, Adas VII CEDYA, (1984), 137-182.
    • (1984) Adas VII CEDYA , pp. 137-182
    • Dlaz, J.I.1    Jlmenez, R.2
  • 26
    • 52549115370 scopus 로고    scopus 로고
    • Sur la contrôlabilité approchée de problèmes paraboliques avec phénomènes d'explosion
    • J. I. DlAZ, J. L. LIONS, Sur la contrôlabilité approchée de problèmes paraboliques avec phénomènes d'explosion, Comptes Rendus Acad. Sci. Paris, Série I, t.327(1998), 173-177.
    • (1998) Comptes Rendus Acad. Sci. Paris, Série i , vol.327 , pp. 173-177
    • Dlaz, J.I.1    Lions, J.L.2
  • 27
    • 18144390927 scopus 로고    scopus 로고
    • On the approximate controllability for some explosive parabolic problems
    • K.-H. HUFFMAN et al. Editors, International Series of Numerical Mathematics, Birkhäuser
    • J. I. DlAZ, J. L. LlONS, On the approximate controllability for some explosive parabolic problems, in Optimal Control of Partial Differential Equations, K.-H. HUFFMAN et al. Editors, International Series of Numerical Mathematics, Vol. 133(1999), Birkhäuser, 115-132.
    • (1999) Optimal Control of Partial Differential Equations , vol.133 , pp. 115-132
    • Dlaz, J.I.1    Llons, J.L.2
  • 30
    • 0000401812 scopus 로고
    • Quasilinear parabolic systems with dynamical boundary conditions
    • J. ESCHER, Quasilinear parabolic systems with dynamical boundary conditions, Comm. P DE; 18(1993), 1309-1364.
    • (1993) Comm. P de , vol.18 , pp. 1309-1364
    • Escher, J.1
  • 31
    • 0345851344 scopus 로고
    • On the density of the range of the semigroup for semilinear heat equations
    • Springer Verlag, New York, IMA
    • C. FAHRE, J. P. PUEL, E. ZUAZUA, On the density of the range of the semigroup for semilinear heat equations. In Control and optimal design of distributed parameter systems, Springer Verlag, New York, IMA Volume 70(1994), 73-92.
    • (1994) Control and Optimal Design of Distributed Parameter Systems , vol.70 , pp. 73-92
    • Fahre, C.1    Puel, J.P.2    Zuazua, E.3
  • 32
    • 84971109212 scopus 로고
    • Approximate controllability for the semilinear heat equations
    • Sect. A.
    • C. FABRE, J. P. PUEL, E. ZUAZUA, Approximate controllability for the semilinear heat equations, Proc Royal Soc. Edinburgh, Sect. A., 125(1995), 31-61.
    • (1995) Proc Royal Soc. Edinburgh , vol.125 , pp. 31-61
    • Fabre, C.1    Puel, J.P.2    Zuazua, E.3
  • 33
    • 0001254093 scopus 로고
    • The parabolic differential equations and the associated semi-groups of transforms
    • W. FELLER, The parabolic differential equations and the associated semi-groups of transforms, Ann. of Math. 55(1952), 468-519.
    • (1952) Ann. of Math. , vol.55 , pp. 468-519
    • Feller, W.1
  • 34
    • 0031257438 scopus 로고    scopus 로고
    • Global Solutions of the Laplace Equation with a Nonlinear Dynamica Boundary Condition
    • M. FlLA, P. QUITTNER, Global Solutions of the Laplace Equation with a Nonlinear Dynamica Boundary Condition, Math. Methods in Appl. Sci., 20(1997), 1325-1333.
    • (1997) Math. Methods in Appl. Sci. , vol.20 , pp. 1325-1333
    • Flla, M.1    Quittner, P.2
  • 35
    • 52549100096 scopus 로고    scopus 로고
    • Modelling Surface Runoff and Infiltration of Rain by an Elliptic
    • Preprint no. 539 Sonderforschungsbereich 256 Nichtlineare Partielle Differentialgleichungen, Rheinishch Friedrich-Wilhems-Universität, Bonn
    • J. FlLO, S. LUCKHAUS, Modelling Surface Runoff and Infiltration of Rain by an EllipticParabolic Equation Coupled with a First Order Equation on the Boundary, Preprint no. 539 Sonderforschungsbereich 256 Nichtlineare Partielle Differentialgleichungen, Rheinishch Friedrich-Wilhems-Universität, Bonn, 1998.
    • (1998) Parabolic Equation Coupled with a First Order Equation on the Boundary
    • Fllo, J.1    Luckhaus, S.2
  • 36
    • 0001278174 scopus 로고
    • The initial value problem for the linearized equations of wate waves
    • A. FRIEDMAN, M. SHINBROT, The initial value problem for the linearized equations of wate waves, J. Math. Mech., 17(1968), 107-180.
    • (1968) J. Math. Mech. , vol.17 , pp. 107-180
    • Friedman, A.1    Shinbrot, M.2
  • 37
    • 84971166919 scopus 로고
    • Two-point boundary value problems with eigenvalue parameter contained i the boundary condition
    • C. T. FULTON, Two-point boundary value problems with eigenvalue parameter contained i the boundary condition, Proc. Royal Soc. Edinburgh, 77A(1977), 293-308.
    • (1977) Proc. Royal Soc. Edinburgh , vol.77 A , pp. 293-308
    • Fulton, C.T.1
  • 38
    • 0342670035 scopus 로고
    • Some backward uniqueness results
    • J.-M. GHIDAGLIA, Some backward uniqueness results, Nonlinear Anal., 10(1986), 777-790.
    • (1986) Nonlinear Anal. , vol.10 , pp. 777-790
    • Ghidaglia, J.-M.1
  • 40
    • 0041619845 scopus 로고
    • Semilinear evolution equations and fractional powers of closed pair of operators
    • M. GROBBELAAR-VAN DALSEN, Semilinear evolution equations and fractional powers of closed pair of operators, Proc. Royal Soc. Edinburgh, 105A(1987), 101-115.
    • (1987) Proc. Royal Soc. Edinburgh , vol.105 A , pp. 101-115
    • Grobbelaar-Van Dalsen, M.1
  • 41
    • 0023573724 scopus 로고
    • Initial boundary value problems from semiconductor device theory
    • K. GROCER, Initial boundary value problems from semiconductor device theory, Z. Angew.Math. Mech., 67(1987), 345-355.
    • (1987) Z. Angew.Math. Mech. , vol.67 , pp. 345-355
    • Grocer, K.1
  • 43
    • 84971154318 scopus 로고
    • Evolution equations with dynamic boundary conditions
    • T. HINTERMANN, Evolution equations with dynamic boundary conditions, Proc. Royal Soc.Edinburgh, 113A(1989), 43-60.
    • (1989) Proc. Royal Soc.Edinburgh , vol.113 A , pp. 43-60
    • Hintermann, T.1
  • 44
    • 0004401647 scopus 로고
    • Nonlinear parabolic equations with the mixed nonlinear and nonstationary boundary conditions
    • J. KACUR, Nonlinear parabolic equations with the mixed nonlinear and nonstationary boundary conditions, Math. Slovaca, 30(1980), 213-237.
    • (1980) Math. Slovaca , vol.30 , pp. 213-237
    • Kacur, J.1
  • 46
    • 0003299184 scopus 로고
    • A problem in diffusion or in the flow of heat for a solid in contact with a fluid
    • R. E. LANGER, A problem in diffusion or in the flow of heat for a solid in contact with a fluid, Tohoku Math., 35(1932), 260-275.
    • (1932) Tohoku Math. , vol.35 , pp. 260-275
    • Langer, R.E.1
  • 47
    • 0003443377 scopus 로고    scopus 로고
    • L. LAPIDUS, N. R. AMUNDSON Editors, Prentice-Hall, Englewoo Cliff's
    • L. LAPIDUS, N. R. AMUNDSON Editors, Chemical Reactor Theory, Prentice-Hall, Englewoo Cliff's, 1997.
    • (1997) Chemical Reactor Theory
  • 49
    • 34250158277 scopus 로고
    • Formal stability of liquid drops
    • ScHLESINGER et al. Editors, World Scientific
    • D. LEWIS, J. MARSDEN, T. RATIU, Formal stability of liquid drops. In Perspectives in Nonlinear Dynamics, ScHLESINGER et al. Editors, World Scientific, 1986, 71-83.
    • (1986) Perspectives in Nonlinear Dynamics , pp. 71-83
    • Lewis, D.1    Marsden, J.2    Ratiu, T.3
  • 54
    • 0003022144 scopus 로고
    • Exact cotrollability for distributed systems. Some trends and some problems
    • R. SlEGLER Editor, Kluwer
    • J. L. LIONS Exact cotrollability for distributed systems. Some trends and some problems. I Applied and Industrial Mathematics, R. SlEGLER Editor, Kluwer, 1991, 59-84.
    • (1991) I Applied and Industrial Mathematics , pp. 59-84
    • Lions, J.L.1
  • 55
    • 36149019686 scopus 로고
    • The diffusion problem for a solid in contact with a stirred liquid
    • H. W. MARCH, W. WEAVER, The diffusion problem for a solid in contact with a stirred liquid, Physical Review, 31(1928), 1072-1082.
    • (1928) Physical Review , vol.31 , pp. 1072-1082
    • March, H.W.1    Weaver, W.2
  • 57
    • 77956939385 scopus 로고
    • Nonstationary or stationary free boundary problems for perfect fluids with surface tension
    • North-Holland, Amsterdam
    • H. OKAMOTO, Nonstationary or stationary free boundary problems for perfect fluids with surface tension, Recent Topics in Nonlinear PDE, Hiroshima 1983, North-Holland, Amsterdam, 1983, 143-154.
    • (1983) Recent Topics in Nonlinear PDE, Hiroshima 1983 , pp. 143-154
    • Okamoto, H.1
  • 59
    • 2942517326 scopus 로고
    • Note on the cooling of a sphere in a mass of well stirred liquid
    • W. PEDDIE, Note on the cooling of a sphere in a mass of well stirred liquid, Proc. Edinburg Math. Soc., 19(1901), 34-35.
    • (1901) Proc. Edinburg Math. Soc. , vol.19 , pp. 34-35
    • Peddie, W.1
  • 60
    • 0013378112 scopus 로고
    • Solutions to a problem in diffusion employing a non-orthogonal sine series
    • R. L. PEEK, Solutions to a problem in diffusion employing a non-orthogonal sine series. Ann.of Mai/i.30,(1929), 265-269.
    • (1929) Ann.of Mai/i. , vol.30 , pp. 265-269
    • Peek, R.L.1
  • 63
    • 52549098809 scopus 로고    scopus 로고
    • Results on approximate controllability for quasilinear diffusion equations
    • Vigo
    • A. M. RAMOS, Results on approximate controllability for quasilinear diffusion equations, Libra de Adas del XV CEDYA, Vol.11, Vigo, (1997), 1129-1134.
    • (1997) Libra de Adas Del XV CEDYA , vol.11 , pp. 1129-1134
    • Ramos, A.M.1
  • 64
    • 84944483089 scopus 로고
    • Theory of the flow of electrons and holes in Germanium and other semiconductors
    • W. VAN ROOSBROECK, Theory of the flow of electrons and holes in Germanium and other semiconductors, Bell Syst, Tech. J., 29(1950), 560-607.
    • (1950) Bell Syst, Tech. J. , vol.29 , pp. 560-607
    • Van Roosbroeck, W.1
  • 65
    • 84976189105 scopus 로고
    • Linear evolution equations in two Banach spaces
    • N. SAUER, Linear evolution equations in two Banach spaces, Proc. Royal Soc. Edinburgh, 91A(1982), 287-303.
    • (1982) Proc. Royal Soc. Edinburgh , vol.91 A , pp. 287-303
    • Sauer, N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.