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Plates with Internal Damping

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Von Karman Evolution Equations

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Abstract

In this chapter von Karman equations with nonlinear internal and fully supported in Ω damping are considered. The boundary conditions associated with the model are either clamped, hinged or else “free”. In this latter case, the boundary conditions may involve naturally both dynamic and nonlinear terms. The well-posedness of solutions to the models considered follows from the results presented in Chapter 3, for models with rotational forces and in Chapter 4, for nonrotational models.

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  1. I. Chueshov, Finite-dimensionality of the attractor in some problems of the nonlinear theory shells, Math. USSR Sbornik, 61 (1988), 411–420.

    Article  MATH  MathSciNet  Google Scholar 

  2. I. Chueshov, Structure of a maximal attractor of a modified system of von Karman equations, J. Soviet Math., 48 (1990), 692–696.

    Article  MATH  MathSciNet  Google Scholar 

  3. I. Chueshov, A problem of nonlinear oscillations of shallow shell in quasistatic formulation, Math. Notes, 47 (1990), 401–407.

    MATH  MathSciNet  Google Scholar 

  4. I. Chueshov, On some continuity property of attractor in a problem on oscillations of shallow shell, In: Dynamical Systems and Complex Analysis, V.A. Marchenko (Ed.), Naukova Dumka, Kiev, 1992, 85–91, in Russian.

    Google Scholar 

  5. I. Chueshov, On a certain system of equations with delay, occurring in aeroelasticity, J. Soviet Math., 58 (1992), 385–390.

    Article  MathSciNet  Google Scholar 

  6. I. Chueshov, On a construction of approximate inertial manifolds for second order in time evolution equations. Nonlinear Anal., 26 (1996), 1007–1021.

    Article  MATH  MathSciNet  Google Scholar 

  7. I. Chueshov, Theory of functionals that uniquely determine asymptotic dynamics of infinite-dimensional dissipative systems, Russian Math. Surv., 53 (1998), 731–776.

    Article  MATH  MathSciNet  Google Scholar 

  8. I. Chueshov, Introduction to the Theory of Infinite-Dimensional Dissipative Systems, Acta, Kharkov, 1999, in Russian; English translation: Acta, Kharkov, 2002; see also http://www.emis.de/monographs/Chueshov/

  9. I. Chueshov, M. Eller and I. Lasiecka, On the attractor for a semilinear wave equation with critical exponent and nonlinear boundary dissipation, Commun. Partial Diff. Eqs., 27 (2002), 1901–1951.

    Article  MATH  MathSciNet  Google Scholar 

  10. I. Chueshov and I. Lasiecka, Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping, Memoirs of AMS, vol.195, no. 912, AMS, Providence, RI, 2008.

    Google Scholar 

  11. M. Daoulatli, I. Lasiecka and D. Toundykov, Uniform energy decay for a wave equation with partially supported nonlinear boundary dissipation without growth restrictions, Discr. Cont. Dyn. Sys., 2 (2009), 67–94.

    MATH  MathSciNet  Google Scholar 

  12. J.M. Ghidaglia and R. Temam, Regularity of the solutions of second order evolution equations and their attractors, Ann. della Scuola Norm. Sup. Pisa, 14 (1987), 485–511.

    MATH  MathSciNet  Google Scholar 

  13. A. K. Khanmamedov, Global attractors for von Karman equations with nonlinear dissipation, J. Math. Anal. Appl., 318 (2006), 92–101.

    Article  MATH  MathSciNet  Google Scholar 

  14. E.A. Krasil’shchikova, The Thin Wing in a Compressible Flow. Nauka, Moscow, 1978, in Russian.

    Google Scholar 

  15. O. Ladyzhenskaya, A dynamical system generated by the Navier–Stokes equations, J. Soviet Math., 3(4) (1975), 458–479.

    Article  MATH  Google Scholar 

  16. I. Lasiecka and W. Heyman, Asymptotic behaviour of solutions in nonlinear dynamic elasti-city, Discr. Cont. Dyn. Syst., 1 (1995), 237–252.

    Article  MATH  MathSciNet  Google Scholar 

  17. I. Lasiecka and A. Ruzmaikina, Finite dimensionality and regularity of attractors for a 2-D semilinear wave equation with nonlinear dissipation, J. Math. Anal. Appl., 270 (2002), 16–50.

    Article  MATH  MathSciNet  Google Scholar 

  18. I. Lasiecka and D. Tataru. Uniform boundary stabilization of semilinear wave equation with nonlinear boundary dissipation. Diff. Integral Eqs., 6 (1993), 507–533.

    MATH  MathSciNet  Google Scholar 

  19. I. Lasiecka and D. Toundykov, Energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms, Nonlin. Anal., 64 (2006), 1757-1797.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanics & Mathematics, Kharkov National University, 61077, Kharkov, Ukraine

    Igor Chueshov

  2. Department of Mathematics, University of Virginia, Charlottesville, Virginia, 22904, USA

    Irena Lasiecka

Authors
  1. Igor Chueshov
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  2. Irena Lasiecka
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Correspondence to Igor Chueshov .

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Chueshov, I., Lasiecka, I. (2010). Plates with Internal Damping. In: Von Karman Evolution Equations. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-87712-9_9

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