Uniform Stabilization of the Petrovsky-Wave Nonlinear coupled system with strong damping

TL;DR

This paper investigates the stability and well-posedness of a nonlinear Petrovsky-Wave coupled system with strong damping, establishing global solutions and energy decay rates.

Contribution

It introduces a novel approach to prove global existence and energy decay for the nonlinear coupled system using Galerkin and multiplier methods.

Findings

Existence of global weak solutions is proven.

Energy decay rate is estimated using multiplier techniques.

The system exhibits uniform stabilization under strong damping.

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.