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Volumn 11, Issue 2-3, 2004, Pages 311-324

Controllability properties of a vibrating string with variable axial load

Author keywords

Axial load; Bilinear control; Controllability; Wave equation

Indexed keywords


EID: 4944232635     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2004.11.311     Document Type: Article
Times cited : (23)

References (18)
  • 2
    • 0018697593 scopus 로고
    • Feedback stabilization of semilinear control systems
    • Ball, J.M.; Slemrod, M (1979): Feedback stabilization of semilinear control systems. Appl. Math. Opt. 5, 169-179.
    • (1979) Appl. Math. Opt. , vol.5 , pp. 169-179
    • Ball, J.M.1    Slemrod, M.2
  • 3
    • 84980193078 scopus 로고
    • Nonharmonic Fourier series and the stabilization of distributed semi-linear control systems
    • Ball, J.M.; Slemrod, M (1979): Nonharmonic Fourier series and the stabilization of distributed semi-linear control systems. Comm. Pure. Appl. Math. 32, 555-587.
    • (1979) Comm. Pure. Appl. Math. , vol.32 , pp. 555-587
    • Ball, J.M.1    Slemrod, M.2
  • 4
    • 0000107228 scopus 로고
    • Controllability for distributed bilinear systems
    • Ball, J.M.; Mardsen, J.E.; Slemrod, M (1982): Controllability for distributed bilinear systems. SIAM J. Contr. Opt. 20, 575-597.
    • (1982) SIAM J. Contr. Opt. , vol.20 , pp. 575-597
    • Ball, J.M.1    Mardsen, J.E.2    Slemrod, M.3
  • 5
    • 0001534477 scopus 로고    scopus 로고
    • Bilinear optimal control of the velocity term in a Kirchhoff plate equation
    • Bradley, M.E.; Lenhart, S.; Yong, J. (1999): Bilinear optimal control of the velocity term in a Kirchhoff plate equation. J. Math. Anal. Appl. 238, 451-467.
    • (1999) J. Math. Anal. Appl. , vol.238 , pp. 451-467
    • Bradley, M.E.1    Lenhart, S.2    Yong, J.3
  • 6
    • 0036014250 scopus 로고    scopus 로고
    • One-sided and internal controllability of semilinear wave equations with infinitely iterated logarithms
    • Cannarsa, P.; Komornik, V.; Loretti, P. (2002): One-sided and internal controllability of semilinear wave equations with infinitely iterated logarithms. Discrete and Continuous Dynamical Systems 8, 745-756.
    • (2002) Discrete and Continuous Dynamical Systems , vol.8 , pp. 745-756
    • Cannarsa, P.1    Komornik, V.2    Loretti, P.3
  • 8
    • 4544284997 scopus 로고    scopus 로고
    • Controllability of some semilinear parabolic problems with multiplicative control
    • San Diego, CA, July 11-14, 2001
    • Fernández, L.A. (2001): Controllability of some semilinear parabolic problems with multiplicative control. Presented at the Fifth SIAM Conference on Control and its applications, San Diego, CA, July 11-14, 2001.
    • (2001) Fifth SIAM Conference on Control and Its Applications
    • Fernández, L.A.1
  • 9
    • 0001140070 scopus 로고    scopus 로고
    • Bilinear control for global controllability of the semilinear parabolic equations with superlinear terms
    • (G. Chen, I. Lasiecka/J. Zhou eds.), Lecture Notes in Pure and Applied Mathematics Marcel Dekker
    • Khapalov, A.Y. (2001): Bilinear control for global controllability of the semilinear parabolic equations with superlinear terms. Control of Nonlinear Distributed Parameter Systems (G. Chen, I. Lasiecka/J. Zhou eds.), 139-155. Lecture Notes in Pure and Applied Mathematics 218. Marcel Dekker.
    • (2001) Control of Nonlinear Distributed Parameter Systems , vol.218 , pp. 139-155
    • Khapalov, A.Y.1
  • 10
    • 0036413811 scopus 로고    scopus 로고
    • Global non-negative controllability of the semilinear parabolic equation governed by bilinear control
    • Khapalov, A.Y. (2002): Global non-negative controllability of the semilinear parabolic equation governed by bilinear control. ESAIM: Contrôle, Optimisation et Calcul des Variations 7, pp. 269-283.
    • (2002) ESAIM: Contrôle, Optimisation et Calcul des Variations , vol.7 , pp. 269-283
    • Khapalov, A.Y.1
  • 11
    • 0347872776 scopus 로고    scopus 로고
    • On bilinear controllability of the parabolic equation with the reaction-diffusion term satisfying Newton's Law
    • Khapalov, A.Y. (2002): On bilinear controllability of the parabolic equation with the reaction-diffusion term satisfying Newton's Law. Computational and Applied Mathematics 21, pp. 1-23.
    • (2002) Computational and Applied Mathematics , vol.21 , pp. 1-23
    • Khapalov, A.Y.1
  • 12
    • 0348220622 scopus 로고    scopus 로고
    • Controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term: A qualitative approach
    • Khapalov, A.Y. (2003): Controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term: A qualitative approach. SIAM J. Control Optim. 41, 1886-1900.
    • (2003) SIAM J. Control Optim. , vol.41 , pp. 1886-1900
    • Khapalov, A.Y.1
  • 13
    • 0029271067 scopus 로고
    • Simultaneous control of a rod equation and a simple Schrödinger equation
    • Kime, K. (1995): Simultaneous control of a rod equation and a simple Schrödinger equation. Systems Control Lett. 24, 301-306.
    • (1995) Systems Control Lett. , vol.24 , pp. 301-306
    • Kime, K.1
  • 14
    • 0011248167 scopus 로고
    • Optimal control of convective-diffusive fluid problem
    • Lenhart, S. (1995): Optimal control of convective-diffusive fluid problem. Math. Models and Methods in Appl. Sci. 5, 225-237.
    • (1995) Math. Models and Methods in Appl. Sci. , vol.5 , pp. 225-237
    • Lenhart, S.1
  • 15
    • 0034360781 scopus 로고    scopus 로고
    • Bilinear optimal control for a wave equation with viscous damping
    • Lenhart, S.; Liang, M. (2002): Bilinear optimal control for a wave equation with viscous damping. Houston J. Math. 26, 575-595.
    • (2002) Houston J. Math. , vol.26 , pp. 575-595
    • Lenhart, S.1    Liang, M.2
  • 16
    • 0033481715 scopus 로고    scopus 로고
    • Bilinear optimal control for a wave equation
    • Liang, M. (1999): Bilinear optimal control for a wave equation. Math. Models Methods Appl. Sci. 9, 45-68.
    • (1999) Math. Models Methods Appl. Sci. , vol.9 , pp. 45-68
    • Liang, M.1
  • 17
    • 0038401228 scopus 로고    scopus 로고
    • Exact controllability in "arbitrarily short time" of the semilinear wave equation
    • Martinez, P.; Vancostenoble, J.: Exact controllability in "arbitrarily short time" of the semilinear wave equation. Discrete and Continuous Dynamical Systems 9, 901-924.
    • Discrete and Continuous Dynamical Systems , vol.9 , pp. 901-924
    • Martinez, P.1    Vancostenoble, J.2
  • 18
    • 38249026535 scopus 로고
    • Strong convergence and arbitrarily slow decay of energy for a class of bilinear control problems
    • Müller, S. (1989): Strong convergence and arbitrarily slow decay of energy for a class of bilinear control problems. J. Differential Equations 81, 50-67.
    • (1989) J. Differential Equations , vol.81 , pp. 50-67
    • Müller, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.