On the Existence and Asymptotic Behavior for a Strongly Damped Nonlinear Coupled Petrovsky-Wave System

Abstract

In this paper, we consider the initial-boundary value problem for a class of nonlinear coupled wave equation and Petrovesky system in a bounded domain. The strong damping is nonlinear. First, we prove the existence of global weak solutions by using the energy method combined with Faedo-Galarkin method and the multiplier method. In addition, under suitable conditions on functions gi(⋅), i = 1, 2 and a(⋅), we obtain both exponential and polynomial decay estimates. The method of proofs is direct and based on the energy method combined with the multipliers technique, on some integral inequalities due to Haraux and Komornik.