메뉴 건너뛰기




Volumn 9, Issue 2, 2009, Pages 267-291

A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems

Author keywords

Carleman estimates; Control; Kalman Condition; Observability; Reaction diffusion systems

Indexed keywords


EID: 67349271058     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-009-0008-8     Document Type: Article
Times cited : (78)

References (24)
  • 1
    • 33646360562 scopus 로고    scopus 로고
    • Null controllability of some reaction-diffusion systems with one control force
    • F. Ammar-Khodja, A. Benabdallah and C. Dupaix, Null controllability of some reaction-diffusion systems with one control force J. Math.Anal.Appl.320 (2006), no. 2, 928-943
    • (2006) J. Math.Anal.Appl. , vol.320 , Issue.2 , pp. 928-943
    • Ammar-Khodja Benabdallah A, F.1    Dupaix, C.2
  • 2
    • 36148959746 scopus 로고    scopus 로고
    • Controllability for a class of reaction-diffusion systems: The generalized Kalman's condition
    • F. Ammar-Khodja, A. Benabdallah, C. Dupaix and M. Gonzá lez-Burgos, Controllability for a class of reaction-diffusion systems: the generalized Kalman's condition, C. R.Acad.Sci. Paris, Ser. I 345 (2007), no. 10, 543-548
    • (2007) C. R.Acad.Sci. Paris, Ser. i , vol.345 , Issue.10 , pp. 543-548
    • Ammar-Khodja Benabdallah Dupaix C A, F.1    Gonzá Lez-Burgos, M.2
  • 4
    • 30844445391 scopus 로고    scopus 로고
    • Null controllability of some systems of parabolic type by one control force
    • F. Ammar-Khodja, A. Benabdallah, C. Dupaix and I. Kostine, Null controllability of some systems of parabolic type by one control force ESAIM Control Optim.Calc.Var.11 (2005), no. 3, 426-448.
    • (2005) ESAIM Control Optim.Calc.Var. , vol.11 , Issue.3 , pp. 426-448
    • Ammar-Khodja Benabdallah Dupaix C A, F.1    Kostine, I.2
  • 5
    • 34548171032 scopus 로고    scopus 로고
    • Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem
    • A. Benabdallah, Y. Dermenjian, J. Le Rousseau, Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem, J. Math.Anal.Appl. 336 (2007), no. 2, 865-887.
    • (2007) J. Math.Anal.Appl. , vol.336 , Issue.2 , pp. 865-887
    • Benabdallah, A.1    Dermenjian, Y.2    Le Rousseau, J.3
  • 6
    • 4344703293 scopus 로고    scopus 로고
    • Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients
    • DOI 10.1051/cocv:2002047
    • A. Doubova, A. Osses, and J.-P. Puel, Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients, ESAIM Control Optim.Calc.Var. 8 (2002), 621-661. (Pubitemid 47611747)
    • (2002) ESAIM - Control, Optimisation and Calculus of Variations , vol.8 , pp. 621-661
    • Doubova, A.1    Osses, A.2    Puel, J.-P.3
  • 7
    • 33749384322 scopus 로고    scopus 로고
    • Null-exact controllability of a semilinear cascade system of parabolic-hyperbolic equations
    • E. Fernández-Cara, M. Gonzá lez-Burgos, L. de Teresa, Null-exact controllability of a semilinear cascade system of parabolic-hyperbolic equations, Commun.Pure Appl.Anal. 5 (2006), no. 3, 637-656.
    • (2006) Commun.Pure Appl.Anal. , vol.5 , Issue.3 , pp. 637-656
    • Fernández-Cara, E.1
  • 9
    • 4944228240 scopus 로고    scopus 로고
    • Null controllability of a cascade system of parabolic-hyperbolic equations
    • E. Fernández-Cara, L. de Teresa, Null controllability of a cascade system of parabolic- hyperbolic equations, Discrete Contin.Dyn. Syst. 11 (2004), no. 2-3, 699-714. (Pubitemid 39332781)
    • (2004) Discrete and Continuous Dynamical Systems , vol.11 , Issue.2-3 , pp. 699-714
    • Fernandez-Cara, E.1    De Teresa, L.2
  • 10
    • 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, Adv. Differential Equations 5 (2000), no. 4-6, 465-514.
    • (2000) Adv. Differential Equations , vol.5 , Issue.4-6 , pp. 465-514
    • Fernández-Cara, E.1
  • 11
    • 0003252621 scopus 로고    scopus 로고
    • Controllability of Evolution Equations
    • Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul
    • A. Fursikov, O. Yu. Imanuvilov, Controllability of Evolution Equations, Lecture Notes Series 34, Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul, 1996.
    • (1996) Lecture Notes Series , vol.34
    • Fursikov, A.1    Yu. Imanuvilov, O.2
  • 12
    • 31144473352 scopus 로고    scopus 로고
    • Controllability results for some nonlinear coupled parabolic systems by one control force
    • M. González-Burgos, R. Pérez-García, M. González-Burgos, R. Pérez-Garcia, Controllability results for some nonlinear coupled parabolic systems by one control force, Asymptot.Anal.46 (2006), no. 2, 123-162. (Pubitemid 43131565)
    • (2006) Asymptotic Analysis , vol.46 , Issue.2 , pp. 123-162
    • Gonzalez-Burgos, M.1    Perez-Garcia, R.2
  • 14
    • 41449104346 scopus 로고    scopus 로고
    • Null controllability of some systems of two parabolic equations with one control force
    • S. Guerrero, Null controllability of some systems of two parabolic equations with one control force, SIAM J. Control Optim. 46, (2007), no. 2, 379-394.
    • (2007) SIAM J. Control Optim. , vol.46 , Issue.2 , pp. 379-394
    • Guerrero, S.1
  • 16
    • 0344629837 scopus 로고    scopus 로고
    • Carleman Inequalities for Parabolic Equations in Sobolev Spaces of Negative Order and Exact Controllability for Semilinear Parabolic Equations
    • O. Yu. Imanuvilov, M. Yamamoto, Carleman inequalities for parabolic equations in Sobolev spaces of negative order and exact controllability for semilinear parabolic equations, Publ.Res.Inst.Math.Sci. 39 (2003), no. 2, 227-274. (Pubitemid 37513269)
    • (2003) Publications of the Research Institute for Mathematical Sciences , vol.39 , Issue.2 , pp. 227-274
    • Imanuvilov, O.Yu.1    Yamamoto, M.2
  • 18
    • 84963255809 scopus 로고
    • Contrôle exact de l'équation de la chaleur
    • G. Lebeau, L. Robbiano, Contrôle exact de l'équation de la chaleur, Comm.Partial Differential Equations 20 (1995), no. 1-2, 335-356.
    • (1995) Comm.Partial Differential Equations , vol.20 , Issue.1-2 , pp. 335-356
    • Lebeau, G.1    Robbiano, L.2
  • 19
    • 20844444551 scopus 로고    scopus 로고
    • Controllability of a system of parabolic equations with non-diagonal diffusion matrix
    • DOI 10.1093/imamci/dni023
    • H. Leiva, Controllability of a system of parabolic equations with non-diagonal diffusion matrix, IMA J. Math.Control Inform. 22 (2005), no. 2, 187-199. (Pubitemid 40858208)
    • (2005) IMA Journal of Mathematical Control and Information , vol.22 , Issue.2 , pp. 187-199
    • Leiva, H.1
  • 20
    • 33845461636 scopus 로고    scopus 로고
    • Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients
    • DOI 10.1016/j.jde.2006.10.005, PII S0022039606004128
    • J. Le Rousseau, Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients, J. Differential Equations 233 (2007), no. 2, 417-447. (Pubitemid 44895111)
    • (2007) Journal of Differential Equations , vol.233 , Issue.2 , pp. 417-447
    • Le Rousseau, J.1
  • 21
    • 0003316678 scopus 로고
    • Semigroups of linear operators and application to partial differential equations
    • Springer-Verlag, New York
    • A. Pazy, Semigroups of linear operators and application to partial differential equations, Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983.
    • (1983) Applied Mathematical Sciences , vol.44
    • Pazy, A.1
  • 22
    • 0038582011 scopus 로고    scopus 로고
    • Insensitizing controls for a semilinear heat equation
    • L. de Teresa, Insensitizing controls for a semilinear heat equation, Comm.Partial Differential Equations 25 (2000), no. 1-2, 39-72.
    • (2000) Comm.Partial Differential Equations , vol.25 , Issue.1-2 , pp. 39-72
    • De Teresa, L.1
  • 23
    • 0026907835 scopus 로고
    • Constructive steering control functions for linear systems and abstract rank conditions
    • R. Triggiani, Constructive steering control functions for linear systems and abstract rank conditions, J. Optim.Theory Appl. 74 (1992), no. 2, 347-367. (Pubitemid 23572798)
    • (1992) Journal of Optimization Theory and Applications , vol.74 , Issue.2 , pp. 347-367
    • Triggiani, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.