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

Nasser-Eddine Tatar

Journal of Applied Mathematics, 2012, vol. 2012, 1-17

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:936140

DOI: 10.1155/2012/936140

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