메뉴 건너뛰기




Volumn 46, Issue 3, 2007, Pages 1022-1051

Local exact boundary controllability for nonlinear wave equations

Author keywords

Local exact boundary controllability; Quasi linear wave equations; Semilinear wave equations; Time optimal

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CONTROL THEORY; CONTROLLABILITY; DIFFERENTIAL EQUATIONS; INITIAL VALUE PROBLEMS; LINEAR EQUATIONS; MATHEMATICAL MORPHOLOGY; MATHEMATICAL TECHNIQUES; NONLINEAR EQUATIONS; NONLINEAR PROGRAMMING; NUMERICAL METHODS; WAVES;

EID: 44649149011     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/060650222     Document Type: Article
Times cited : (23)

References (25)
  • 1
    • 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
  • 2
    • 34547352888 scopus 로고    scopus 로고
    • Exact controllability of the wave equation with mixed boundary condition and time-dependent coefficients
    • M. M. CAVALCANTI, Exact controllability of the wave equation with mixed boundary condition and time-dependent coefficients, Arch. Math. (Brno), 35 (1999), pp. 29-57.
    • (1999) Arch. Math. (Brno) , vol.35 , pp. 29-57
    • CAVALCANTI, M.M.1
  • 3
    • 0021818126 scopus 로고
    • Energy methods for quasilinear hyperbolic initial-boundary value problems. Applications to elastodynamics
    • C. M. DAFERMOS AND W. J. HRUSA, Energy methods for quasilinear hyperbolic initial-boundary value problems. Applications to elastodynamics, Arch. Rational Mech. Anal., 87 (1985), pp. 267-292.
    • (1985) Arch. Rational Mech. Anal , vol.87 , pp. 267-292
    • DAFERMOS, C.M.1    HRUSA, W.J.2
  • 5
    • 46749128822 scopus 로고    scopus 로고
    • Exact controllability for multidimensional semilinear hyperbolic equations
    • to appear
    • X. FU, J. YONG, AND X. ZHANG, Exact controllability for multidimensional semilinear hyperbolic equations, SIAM J. Control Optim., to appear.
    • SIAM J. Control Optim
    • FU, X.1    YONG, J.2    ZHANG, X.3
  • 6
    • 0017428498 scopus 로고
    • Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
    • T. J. R. HUGHES, T. KATO, AND J. E. MARSDEN, Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity, Arch. Rational Mech. Anal., 63 (1976), pp. 273-294.
    • (1976) Arch. Rational Mech. Anal , vol.63 , pp. 273-294
    • HUGHES, T.J.R.1    KATO, T.2    MARSDEN, J.E.3
  • 7
    • 44649189039 scopus 로고
    • Exact boundary value controllability of a class of hyperbolic equations
    • J. LAGNESE, Exact boundary value controllability of a class of hyperbolic equations, SIAM J. Control Optim., 16 (1978), pp. 1000-1017.
    • (1978) SIAM J. Control Optim , vol.16 , pp. 1000-1017
    • LAGNESE, J.1
  • 8
    • 0002621804 scopus 로고
    • Exact controllability of semilinear abstract systems with applications to waves and plates boundary control problems
    • I. LASIECKA AND R. TRIGGIANI, Exact controllability of semilinear abstract systems with applications to waves and plates boundary control problems, Appl. Math. Optim., 23 (1991), pp. 109-154.
    • (1991) Appl. Math. Optim , vol.23 , pp. 109-154
    • LASIECKA, I.1    TRIGGIANI, R.2
  • 9
    • 44649148241 scopus 로고    scopus 로고
    • I. LASIECKA, R. TRIGGIANI, AND X. ZHANG, Nonconservative wave equations with unobserved Neumann B.C.: Global uniqueness and observability in one shot, in Differential Geometric Methods in the Control of Partial Differential Equations (Boulder, CO, 1999), Contemp. Math. 268, AMS, Providence, RI, 2000, pp. 227-325.
    • I. LASIECKA, R. TRIGGIANI, AND X. ZHANG, Nonconservative wave equations with unobserved Neumann B.C.: Global uniqueness and observability in one shot, in Differential Geometric Methods in the Control of Partial Differential Equations (Boulder, CO, 1999), Contemp. Math. 268, AMS, Providence, RI, 2000, pp. 227-325.
  • 10
    • 44649091143 scopus 로고    scopus 로고
    • Trends in Partial Differential Equations of Mathematical Physics, Progr. Nonlinear Differential Equations Appl. 61, Birkhäuser, Basel
    • T. T. LI, Exact boundary controllability for quasilinear wave equations, in Trends in Partial Differential Equations of Mathematical Physics, Progr. Nonlinear Differential Equations Appl. 61, Birkhäuser, Basel, 2005, pp. 149-160.
    • (2005) Exact boundary controllability for quasilinear wave equations , pp. 149-160
    • LI, T.T.1
  • 11
    • 2142851359 scopus 로고
    • Pitman Monogr. Surveys Pure Appl. Math. 45, Longman Scientific & Technical, Harlow, John Wiley & Sons, New York
    • T. T. LI AND Y. M. CHEN, Global Classical Solutions for Nonlinear Evolution Equations, Pitman Monogr. Surveys Pure Appl. Math. 45, Longman Scientific & Technical, Harlow, John Wiley & Sons, New York, 1992.
    • (1992) Global Classical Solutions for Nonlinear Evolution Equations
    • LI, T.T.1    CHEN, Y.M.2
  • 12
    • 0141580730 scopus 로고    scopus 로고
    • Exact boundary controllability for quasi-linear hyperbolic systems
    • T.-T. LI AND B.-P. RAO, Exact boundary controllability for quasi-linear hyperbolic systems, SIAM J. Control Optim., 41 (2003), pp. 1748-1755.
    • (2003) SIAM J. Control Optim , vol.41 , pp. 1748-1755
    • LI, T.-T.1    RAO, B.-P.2
  • 13
    • 34249080060 scopus 로고    scopus 로고
    • Exact boundary controllability for I-D quasilinear wave equations
    • T. T. LI AND L. X. YU, Exact boundary controllability for I-D quasilinear wave equations, SIAM J. Control Optim., 45 (2006), pp. 1074-1083.
    • (2006) SIAM J. Control Optim , vol.45 , pp. 1074-1083
    • LI, T.T.1    YU, L.X.2
  • 14
    • 0001443929 scopus 로고
    • Controlabilité exacte des systèmes distribués (Exact controllability of distributed systems)
    • J. L. LIONS, Controlabilité exacte des systèmes distribués (Exact controllability of distributed systems), 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
  • 15
    • 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
  • 16
    • 84961355905 scopus 로고
    • A unified boundary controllability theory for hyperbolic and parabolic partial differential equations
    • D. L. 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.L.1
  • 17
    • 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
  • 18
    • 0001692117 scopus 로고    scopus 로고
    • Carleman estimates and unique continuation for solutions to boundary value problems
    • D. TATARU, Carleman estimates and unique continuation for solutions to boundary value problems, J. Math. Pures Appl. (9), 75 (1996), pp. 367-408.
    • (1996) J. Math. Pures Appl. (9) , vol.75 , pp. 367-408
    • TATARU, D.1
  • 19
    • 44649150088 scopus 로고    scopus 로고
    • M. E. TAYLOR, Partial Differential Equations. I. Basic Theory, Appl. Math. Sci. 115, Springer-Verlag, New York, 1996.
    • M. E. TAYLOR, Partial Differential Equations. I. Basic Theory, Appl. Math. Sci. 115, Springer-Verlag, New York, 1996.
  • 20
    • 44649126581 scopus 로고    scopus 로고
    • M. E. TAYLOR, Partial Differential Equations. III. Nonlinear Equations, Appl. Math. Sci. 115, Springer-Verlag, New York, 1996.
    • M. E. TAYLOR, Partial Differential Equations. III. Nonlinear Equations, Appl. Math. Sci. 115, Springer-Verlag, New York, 1996.
  • 21
    • 0033140929 scopus 로고    scopus 로고
    • On the observability inequalities for exact controllability of wave equations with variable coefficients
    • P.-F. YAO, On the observability inequalities for exact controllability of wave equations with variable coefficients, SIAM J. Control Optim., 37 (1999), pp. 1568-1599.
    • (1999) SIAM J. Control Optim , vol.37 , pp. 1568-1599
    • YAO, P.-F.1
  • 23
    • 84979053439 scopus 로고    scopus 로고
    • Exact boundary controllability for higher order quasilinear hyperbolic equations
    • L. X. YU, Exact boundary controllability for higher order quasilinear hyperbolic equations, Appl. Math. J. Chinese Univ. Ser. B, 20 (2005), pp. 127-141.
    • (2005) Appl. Math. J. Chinese Univ. Ser. B , vol.20 , pp. 127-141
    • YU, L.X.1
  • 24
    • 0003138438 scopus 로고
    • Exact controllability for the semilinear wave equation
    • E. ZUAZUA, Exact controllability for the semilinear wave equation, J. Math. Pures Appl. (9), 69 (1990), pp. 1-31.
    • (1990) J. Math. Pures Appl. (9) , vol.69 , pp. 1-31
    • ZUAZUA, E.1
  • 25
    • 85012981810 scopus 로고
    • Exact controllability for semilinear wave equations in one space dimension
    • E. ZUAZUA, Exact controllability for semilinear wave equations in one space dimension, Ann. Inst. H. Poincaré Anal. Non Linéaire, 10 (1993), pp. 109-129.
    • (1993) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.10 , pp. 109-129
    • ZUAZUA, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.