UNIFORM STABILIZATION OF THE PETROVSKY-WAVE NONLINEAR COUPLED SYSTEM WITH STRONG DAMPING

UNIFORM STABILIZATION OF THE PETROVSKY-WAVE NONLINEAR COUPLED SYSTEM WITH STRONG DAMPING

A. Ben Aissa

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Abstract

This paper concerns the well-posedness and uniform stabilization of the Petrovsky-Wave Nonlinear coupled system with strong damping. Existence of global weak solutions for this problem is established by using the Galerkin method. Meanwhile, under a clever use of the multiplier method, we estimate the total energy decay rate.

Keywords

Coupled systems, strong damping, Well-posedness, Faedo-Galerkin method.