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Volumn 46, Issue 6, 2007, Pages 2071-2095

Exact controllability for the time dependent transport equation

Author keywords

Carleman estimate; Exact controllability; Transport equation

Indexed keywords

CARLEMAN ESTIMATE; EXACT CONTROLLABILITIES; EXACT CONTROLLABILITY; TIME DEPENDENTS; TRANSPORT EQUATION; TRANSPORT EQUATIONS;

EID: 55349111858     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/060652804     Document Type: Article
Times cited : (38)

References (38)
  • 1
    • 0000469206 scopus 로고
    • Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; théorèmes d'approximation; applications à l'équations de tranport
    • C. BARDOS, Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; théorèmes d'approximation; applications à l'équations de tranport, Ann. Sci. École Norm. Sup. (4), 3 (1970), pp. 185-233.
    • (1970) Ann. Sci. École Norm. Sup. (4) , vol.3 , pp. 185-233
    • BARDOS, C.1
  • 2
    • 0026923885 scopus 로고
    • Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary
    • C. BARDOS, G. LEBEAU, AND J. RAUCH, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, SIAM J. Control Optim., 30 (1992), pp. 1024-1065.
    • (1992) SIAM J. Control Optim , vol.30 , pp. 1024-1065
    • BARDOS, C.1    LEBEAU, G.2    RAUCH, J.3
  • 4
    • 0000634876 scopus 로고    scopus 로고
    • Time-resolved fluorescence and photon migration studies in biomedical and model random media
    • B. B. DAS, F. LIU, AND R. R. ALFANO, Time-resolved fluorescence and photon migration studies in biomedical and model random media, Rep. Progr. Phys., 60 (1997), pp. 227-292.
    • (1997) Rep. Progr. Phys , vol.60 , pp. 227-292
    • DAS, B.B.1    LIU, F.2    ALFANO, R.R.3
  • 6
    • 33144467505 scopus 로고
    • The solutions of multidimensional generalized transport equations and their calculation by difference methods
    • Academic Press, New York
    • A. DOUGLIS, The solutions of multidimensional generalized transport equations and their calculation by difference methods, in Numerical Solution of Partial Differential Equations, Academic Press, New York, 1966, pp. 197-256.
    • (1966) Numerical Solution of Partial Differential Equations , pp. 197-256
    • DOUGLIS, A.1
  • 7
    • 0003405647 scopus 로고
    • Linear Operators. Part I
    • John Wiley & Sons, New York
    • N. DUNFORD AND J. T. SCHWARTZ, Linear Operators. Part I. General Theory, John Wiley & Sons, New York, 1964.
    • (1964) General Theory
    • DUNFORD, N.1    SCHWARTZ, J.T.2
  • 8
    • 23944464441 scopus 로고    scopus 로고
    • Exact controllability of electromagnetic fields in a general region
    • M. ELLER AND J. E. MASTERS, Exact controllability of electromagnetic fields in a general region, Appl. Math. Optim., 45 (2002), pp. 99-123.
    • (2002) Appl. Math. Optim , vol.45 , pp. 99-123
    • ELLER, M.1    MASTERS, J.E.2
  • 11
    • 55349110557 scopus 로고    scopus 로고
    • R. GULLIVER, I. LASIECKA, W. LITTMAN, AND R. TRIGGIANI, The case for differential geometry in the control of single and coupled PDEs: The structural acoustic chamber, in IMA Math. Appl. 137, Springer-Verlag, Berlin, 2004, pp. 73-181.
    • R. GULLIVER, I. LASIECKA, W. LITTMAN, AND R. TRIGGIANI, The case for differential geometry in the control of single and coupled PDEs: The structural acoustic chamber, in IMA Vol. Math. Appl. 137, Springer-Verlag, Berlin, 2004, pp. 73-181.
  • 12
    • 0001490384 scopus 로고
    • Observabilité frontière de l'équation des ondes
    • L. F. HI, Observabilité frontière de l'équation des ondes, C.R. Acad. Sci. Paris Sér. I Math., 302 (1986), pp. 443-446.
    • (1986) C.R. Acad. Sci. Paris Sér. I Math , vol.302 , pp. 443-446
    • HI, L.F.1
  • 14
    • 0348081503 scopus 로고
    • Boundary controllability of parabolic equations
    • O. YU. IMANUVILOV, Boundary controllability of parabolic equations, Sbornik Math., 186 (1995), pp. 879-900.
    • (1995) Sbornik Math , vol.186 , pp. 879-900
    • YU. IMANUVILOV, O.1
  • 15
    • 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 AND 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), pp. 227-274.
    • (2003) Publ. Res. Inst. Math. Sci , vol.39 , pp. 227-274
    • YU. IMANUVILOV, O.1    YAMAMOTO, M.2
  • 17
    • 0002267569 scopus 로고
    • Stability estimates for ill-posed Cauchy problem involving hyperbolic equations and inequalities
    • M. KAZEMI AND M. V. KLIBANOV, Stability estimates for ill-posed Cauchy problem involving hyperbolic equations and inequalities, Appl. Anal., 50 (1993), pp. 93-102.
    • (1993) Appl. Anal , vol.50 , pp. 93-102
    • KAZEMI, M.1    KLIBANOV, M.V.2
  • 18
    • 0347940923 scopus 로고
    • Newton-Kantorovich method for 3-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time dependent data
    • M. V. KLIBANOV AND J. MALINSKY, Newton-Kantorovich method for 3-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time dependent data, Inverse Problems, 7 (1991), pp. 577-595.
    • (1991) Inverse Problems , vol.7 , pp. 577-595
    • KLIBANOV, M.V.1    MALINSKY, J.2
  • 20
    • 33744541833 scopus 로고    scopus 로고
    • Lipschitz stability of a non-standard problem for the non-stationary transport equation via Carleman estimate
    • M. V. KLIBANOV AND S. E. PAMYATNYKH, Lipschitz stability of a non-standard problem for the non-stationary transport equation via Carleman estimate, Inverse Problems, 22 (2006), pp. 881-890.
    • (2006) Inverse Problems , vol.22 , pp. 881-890
    • KLIBANOV, M.V.1    PAMYATNYKH, S.E.2
  • 23
    • 0038689589 scopus 로고
    • Course of Theoretical Physics
    • Pergamon Press, New York
    • L. D. LANDAU AND E. M. LIFSHITZ, Course of Theoretical Physics. Volume 10. Physical Kinetics, Pergamon Press, New York, 1981.
    • (1981) Physical Kinetics , vol.10
    • LANDAU, L.D.1    LIFSHITZ, E.M.2
  • 24
    • 36849113737 scopus 로고
    • Asymptotic solution of neutron transport problems for small mean free paths
    • E. W. LARSEN AND J. B. KELLER, Asymptotic solution of neutron transport problems for small mean free paths, J. Math. Phys., 15 (1974), pp. 75-81.
    • (1974) J. Math. Phys , vol.15 , pp. 75-81
    • LARSEN, E.W.1    KELLER, J.B.2
  • 25
    • 0000688307 scopus 로고
    • Exact controllability of the wave equation with Neumann boundary control
    • I. LASIECKA AND R. TRIGGIANI, Exact controllability of the wave equation with Neumann boundary control, Appl. Math. Optim., 19 (1989), pp. 243-290.
    • (1989) Appl. Math. Optim , vol.19 , pp. 243-290
    • LASIECKA, I.1    TRIGGIANI, R.2
  • 27
    • 0001443929 scopus 로고
    • Contrôlabilité exacte des systèmes distribués
    • J. L. LIONS, Contrôlabilité exacte des systèmes distribués, C. R. Acad. Sci. Paris Sér. I Math., 302 (1986), pp. 471-475.
    • (1986) C. R. Acad. Sci. Paris Sér. I Math , vol.302 , pp. 471-475
    • LIONS, J.L.1
  • 28
    • 0023966723 scopus 로고
    • Exact controllability, stabilization and perturbations for distributed systems
    • J. L. LIONS, Exact controllability, stabilization and perturbations for distributed systems, SIAM Rev., 30 (1988), pp. 1-68.
    • (1988) SIAM Rev , vol.30 , pp. 1-68
    • LIONS, J.L.1
  • 31
    • 18644378486 scopus 로고
    • Inverse problems for the determination of a coefficient and the right side of a nonstationary multivelocity transport equation with overdetermination at a point
    • A. I. PRILEPKO AND A. L. IVANKOV, Inverse problems for the determination of a coefficient and the right side of a nonstationary multivelocity transport equation with overdetermination at a point, Differ. Equ., 21 (1985), pp. 88-96.
    • (1985) Differ. Equ , vol.21 , pp. 88-96
    • PRILEPKO, A.I.1    IVANKOV, A.L.2
  • 32
    • 84961355905 scopus 로고
    • A unified boundary controllability theory for hyperbolic and parabolic partial differential equations
    • D. I. RUSSELL, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations, Stud. Appl. Math., 52 (1973), pp. 189-211.
    • (1973) Stud. Appl. Math , vol.52 , pp. 189-211
    • RUSSELL, D.I.1
  • 33
    • 21144456777 scopus 로고
    • Observation and prediction for the heat equation
    • T. J. SEIDMAN, Observation and prediction for the heat equation, III, J. Differential Equations, 20 (1976), pp. 18-27.
    • (1976) III, J. Differential Equations , vol.20 , pp. 18-27
    • SEIDMAN, T.J.1
  • 34
    • 0001406093 scopus 로고
    • -1 (Ω) of the wave equation with Dirichlet boundary control acting on a portion of the boundary
    • -1 (Ω) of the wave equation with Dirichlet boundary control acting on a portion of the boundary, Appl. Math. Optim., 18 (1988), pp. 241-277.
    • (1988) Appl. Math. Optim , vol.18 , pp. 241-277
    • TRIGGIANI, R.1
  • 35
    • 55349127323 scopus 로고
    • Sangyo-tosyo, Tokyo, in Japanese
    • S. UKAI, Transport Equations, Sangyo-tosyo, Tokyo, 1976 (in Japanese).
    • (1976) Transport Equations
    • UKAI, S.1
  • 36
    • 77957066266 scopus 로고
    • Solutions of Boltzmann equations
    • North-Holland, Amsterdam
    • S. UKAI, Solutions of Boltzmann equations, in Patterns and Waves, North-Holland, Amsterdam, 1986, pp. 37-96.
    • (1986) Patterns and Waves , pp. 37-96
    • UKAI, S.1
  • 37
    • 4043105065 scopus 로고    scopus 로고
    • G. WANG, Y. LI, AND M. JIANG, Uniqueness theorems in bioluminescence tomography, Med. Phys., 31 (2004), pp. 2289-2299; Erratum: Med. Phys., 32 (2005), p. 3059.
    • G. WANG, Y. LI, AND M. JIANG, Uniqueness theorems in bioluminescence tomography, Med. Phys., 31 (2004), pp. 2289-2299; Erratum: Med. Phys., 32 (2005), p. 3059.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.