Journal of Applied Mathematics

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

Nasser-Eddine Tatar

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 936140, 17 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495261

Digital Object Identifier
doi:10.1155/2012/936140

Mathematical Reviews number (MathSciNet)
MR2960005

Zentralblatt MATH identifier
1255.35184

Citation

Tatar, Nasser-Eddine. Asymptotic Behavior for a Nondissipative and Nonlinear System of the Kirchhoff Viscoelastic Type. J. Appl. Math. 2012 (2012), Article ID 936140, 17 pages. doi:10.1155/2012/936140. https://projecteuclid.org/euclid.jam/1355495261


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