Weak Decay Stability Control on a Class of Quasilinear Wave Equations

Abstract

In this paper, we concerned with the weak decay stability on a class of quasi-linear wave equations. We use a so-called energy perturbation method to establish weak controllability of solutions in terms of energy norm for a class of nonlinear functions. We shall devise a new approach to show the weak decay controllability with the help of differential inequalities by estimating the relationship between energy inequalities and attenuating property of weak solutions; by using a perturbation of energy, we will derive differential inequalities, and determine the small positive number ε.