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Asymptotic Behavior for a Nondissipative and Nonlinear System of the Kirchhoff Viscoelastic Type

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  • Nasser-Eddine Tatar

Abstract

A wave equation of the Kirchhoff type with several nonlinearities is stabilized by a viscoelastic damping. We consider the case of nonconstant (and unbounded) coefficients. This is a nondissipative case, and as a consequence the nonlinear terms cannot be estimated in the usual manner by the initial energy. We suggest a way to get around this difficulty. It is proved that if the solution enters a certain region, which we determine, then it will be attracted exponentially by the equilibrium.

Suggested Citation

  • Nasser-Eddine Tatar, 2012. "Asymptotic Behavior for a Nondissipative and Nonlinear System of the Kirchhoff Viscoelastic Type," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, August.
  • Handle: RePEc:hin:jnljam:936140
    DOI: 10.1155/2012/936140
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