Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2012 (2012), Article ID 936140, 17 pages.
Asymptotic Behavior for a Nondissipative and Nonlinear System of the Kirchhoff Viscoelastic Type
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.
J. Appl. Math., Volume 2012 (2012), Article ID 936140, 17 pages.
First available in Project Euclid: 14 December 2012
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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