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Volumn 48, Issue 3, 2009, Pages 1632-1659

Solving inverse source problems using observability. Applications to the euler-bernoulli plate equation

Author keywords

Exact observability; Inverse source problem; Plate equation

Indexed keywords

ABSTRACT THEORY; EULER-BERNOULLI PLATE EQUATION; EXACT OBSERVABILITY; IDENTIFIABILITY; INFINITE-DIMENSIONAL SYSTEM; INVERSE SOURCE PROBLEM; PLATE EQUATION; PLATE EQUATIONS; POINT SOURCES; SOURCE TERMS;

EID: 67649253178     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/080725635     Document Type: Article
Times cited : (31)

References (30)
  • 2
    • 3042858222 scopus 로고    scopus 로고
    • On the determination of point-forces on a Stokes system
    • C. J. S. ALVES AND A. L. SILVESTRE, On the determination of point-forces on a Stokes system, Math. Comput. Simulation, 66 (2004), pp. 385-397.
    • (2004) Math. Comput. Simulation , vol.66 , pp. 385-397
    • ALVES, C.J.S.1    SILVESTRE, A.L.2
  • 3
    • 0008719126 scopus 로고
    • Un exemple d'utilisation des notions de propagation pour le controle et la stabilisation de problemes hyperboliques
    • C. BARDOS, G. LEBEAU, AND J. RAUCH, Un exemple d'utilisation des notions de propagation pour le controle et la stabilisation de problemes hyperboliques, Rend. Sem. Mat. Univ. Politec. Torino, 1988, Special Issue (1989), pp. 11-31.
    • (1989) Rend. Sem. Mat. Univ. Politec. Torino, 1988 , Issue.SPEC. ISSUE , pp. 11-31
    • BARDOS, C.1    LEBEAU, G.2    RAUCH, J.3
  • 4
    • 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
  • 6
    • 27844449058 scopus 로고    scopus 로고
    • Contrôlabilité exacte des ondes dans des ouverts peu réguliers
    • N. BURQ, Contrôlabilité exacte des ondes dans des ouverts peu réguliers, Asymptot. Anal., 14 (1997), pp. 157-191.
    • (1997) Asymptot. Anal , vol.14 , pp. 157-191
    • BURQ, N.1
  • 7
    • 0141827477 scopus 로고    scopus 로고
    • Contrôle de l'équation des ondes dans des ouverts comportant des coins
    • N. BURQ, Contrôle de l'équation des ondes dans des ouverts comportant des coins, Bull. Soc. Math. France, 126 (1998), pp. 601-637.
    • (1998) Bull. Soc. Math. France , vol.126 , pp. 601-637
    • BURQ, N.1
  • 8
    • 67649290615 scopus 로고    scopus 로고
    • S. DOLECKI AND D. L. RUSSELL, A general theory of observation and control., SIAM J. Control Optim., 15 (1977), pp. 185-220.
    • S. DOLECKI AND D. L. RUSSELL, A general theory of observation and control., SIAM J. Control Optim., 15 (1977), pp. 185-220.
  • 9
    • 84968496765 scopus 로고
    • On majorization, factorization, and range inclusion of operators on Hilbert space
    • R. G. DOUGLAS, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc., 17 (1966), pp. 413-415.
    • (1966) Proc. Amer. Math. Soc , vol.17 , pp. 413-415
    • DOUGLAS, R.G.1
  • 10
    • 0035418946 scopus 로고    scopus 로고
    • Determination of point wave sources by boundary measurements
    • A. EL BADIA AND T. HA-DUONG, Determination of point wave sources by boundary measurements, Inverse Problems, 17 (2001), pp. 1127-1139.
    • (2001) Inverse Problems , vol.17 , pp. 1127-1139
    • EL BADIA, A.1    HA-DUONG, T.2
  • 11
    • 0037264225 scopus 로고    scopus 로고
    • On an inverse source problem for the heat equation. Application to a pollution detection problem
    • A. EL BADIA AND T. HA-DUONG, On an inverse source problem for the heat equation. Application to a pollution detection problem, J. Inverse Ill-Posed Probl., 10 (2002), pp. 585-599.
    • (2002) J. Inverse Ill-Posed Probl , vol.10 , pp. 585-599
    • EL BADIA, A.1    HA-DUONG, T.2
  • 13
    • 0036537477 scopus 로고    scopus 로고
    • Upper and lower estimates in determining point sources in a wave equation
    • V. KOMORNIK AND M. YAMAMOTO, Upper and lower estimates in determining point sources in a wave equation, Inverse Problems, 18 (2002), pp. 319-329.
    • (2002) Inverse Problems , vol.18 , pp. 319-329
    • KOMORNIK, V.1    YAMAMOTO, M.2
  • 14
    • 28544435013 scopus 로고    scopus 로고
    • Estimation of point sources and applications to inverse problems
    • V. KOMORNIK AND M. YAMAMOTO, Estimation of point sources and applications to inverse problems, Inverse Problems, 21 (2005), pp. 2051-2070.
    • (2005) Inverse Problems , vol.21 , pp. 2051-2070
    • KOMORNIK, V.1    YAMAMOTO, M.2
  • 15
    • 84942912012 scopus 로고
    • Appl. Math. Sci. 82, Springer-Verlag, Berlin
    • R. KRESS, Linear Integral Equations, Appl. Math. Sci. 82, Springer-Verlag, Berlin, 1989.
    • (1989) Linear Integral Equations
    • KRESS, R.1
  • 16
    • 0000977450 scopus 로고
    • Controledel'equation de Schrodinger
    • G. LEBEAU, Controledel'equation de Schrodinger, J. Math. Pures Appl. (9), 71 (1992), pp. 267-291.
    • (1992) J. Math. Pures Appl. (9) , vol.71 , pp. 267-291
    • LEBEAU, G.1
  • 17
    • 55849100894 scopus 로고    scopus 로고
    • Identifiability, stability and reconstruction results of point sources by boundary measurements in heteregeneous trees
    • S. NICAISE AND O. ZAÏR, Identifiability, stability and reconstruction results of point sources by boundary measurements in heteregeneous trees, Rev. Mat. Complut., 16 (2003), pp. 151-178.
    • (2003) Rev. Mat. Complut , vol.16 , pp. 151-178
    • NICAISE, S.1    ZAÏR, O.2
  • 18
    • 3042536925 scopus 로고    scopus 로고
    • Determination of point sources in vibrating beams by boundary measurements: Identifiability, stability, and reconstruction results
    • S. NLCAISE AND O. ZAÏR, Determination of point sources in vibrating beams by boundary measurements: Identifiability, stability, and reconstruction results, Electron. J. Differential Equations, No. 20 (2004).
    • (2004) Electron. J. Differential Equations , Issue.20
    • NLCAISE, S.1    ZAÏR, O.2
  • 19
    • 67649262885 scopus 로고    scopus 로고
    • J.-P. PUEL AND M. YAMAMOTO, Applications de la controiabiliteexacte a quelques problemes inverses hyperboliques, C.R.Acad. Sci. ParisSer. I Math., 320 (1995), pp. 1171-1176.
    • J.-P. PUEL AND M. YAMAMOTO, Applications de la controiabiliteexacte a quelques problemes inverses hyperboliques, C.R.Acad. Sci. ParisSer. I Math., 320 (1995), pp. 1171-1176.
  • 20
    • 84967773649 scopus 로고
    • Infinite-dimensional linear systems with unbounded control and observation: A functional analytical approach
    • D. SALAMON, Infinite-dimensional linear systems with unbounded control and observation: A functional analytical approach, Trans. Amer. Math. Soc., 300 (1987), pp. 383-431.
    • (1987) Trans. Amer. Math. Soc , vol.300 , pp. 383-431
    • SALAMON, D.1
  • 21
    • 0003183926 scopus 로고
    • Realization theory in Hilbert space
    • D. SALAMON, Realization theory in Hilbert space, Math. Systems Theory, 21 (1989), pp. 147-164.
    • (1989) Math. Systems Theory , vol.21 , pp. 147-164
    • SALAMON, D.1
  • 22
    • 67649241481 scopus 로고    scopus 로고
    • Fast and strongly localized observation for the Schrödinger equation
    • G. TENENBAUM AND M. TUCSNAK, Fast and strongly localized observation for the Schrödinger equation, Trans. Amer. Math. Soc., 361 (2009), pp. 951-977.
    • (2009) Trans. Amer. Math. Soc , vol.361 , pp. 951-977
    • TENENBAUM, G.1    TUCSNAK, M.2
  • 23
    • 0033708463 scopus 로고    scopus 로고
    • Simultaneous exact controllability and some applicatAons,SIAM J
    • M. TUCSNAK AND G. WEISS, Simultaneous exact controllability and some applicatAons,SIAM J. Control Optim., 38 (2000), pp. 1408-1427.
    • (2000) Control Optim , vol.38 , pp. 1408-1427
    • TUCSNAK, M.1    WEISS, G.2
  • 24
    • 64149096180 scopus 로고    scopus 로고
    • Observation and Control for Operator Semigroups
    • Birkhauser, Basel, also available online from
    • M. TUCSNAK AND G. WEISS, Observation and Control for Operator Semigroups,Birkhauser Advanced Texts, Birkhauser, Basel, 2009; also available online from http://www.iecn.u-nancy.fr/~tucsnak/obsbook.pdf.
    • (2009) Birkhauser Advanced Texts
    • TUCSNAK, M.1    WEISS, G.2
  • 25
    • 33847649585 scopus 로고    scopus 로고
    • Global uniqueness and stability for an inverse plate problem
    • Y. H. WANG, Global uniqueness and stability for an inverse plate problem, J. Optim. Theory Appl., 132 (2007), pp. 161-173.
    • (2007) J. Optim. Theory Appl , vol.132 , pp. 161-173
    • WANG, Y.H.1
  • 26
    • 0001788805 scopus 로고
    • Regular linear systems with feedback
    • G. WEISS, Regular linear systems with feedback, Math. Control Signals Systems, 7 (1994), pp. 23-57.
    • (1994) Math. Control Signals Systems , vol.7 , pp. 23-57
    • WEISS, G.1
  • 27
    • 84966260365 scopus 로고
    • Transfer functions of regular linear systems, Part I: Characterizations of regularity
    • G. WEISS, Transfer functions of regular linear systems, Part I: Characterizations of regularity, Trans. Amer. Math. Soc., 342 (1994), pp. 827-854.
    • (1994) Trans. Amer. Math. Soc , vol.342 , pp. 827-854
    • WEISS, G.1
  • 29
    • 0001147202 scopus 로고
    • Stability, reconstruction formula and regularization for an inverse source hyperbolic problem by a control method
    • M. YAMAMOTO, Stability, reconstruction formula and regularization for an inverse source hyperbolic problem by a control method, Inverse Problems, 11 (1995), pp. 481-496.
    • (1995) Inverse Problems , vol.11 , pp. 481-496
    • YAMAMOTO, M.1
  • 30
    • 0032622981 scopus 로고    scopus 로고
    • Uniqueness and stability in multidimensional hyperbolic inverse problems
    • M. YAMAMOTO, Uniqueness and stability in multidimensional hyperbolic inverse problems,J. Math. Pures Appl. (9), 78 (1999), pp. 65-98.
    • (1999) J. Math. Pures Appl. (9) , vol.78 , pp. 65-98
    • YAMAMOTO, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.