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

Abstract EN

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.