Time-weighted energy method for quasi-linear hyperbolic systems of viscoelasticity

Abstract

The aim in this paper is to develop the time-weighted energy method for quasi-linear hyperbolic systems of viscoelasticity. As a consequence, we prove the global existence and decay estimate of solutions for the space dimension $n\geq 2$, provided that the initial data are small in the $L^{2}$-Sobolev space.