Decay estimates of solutions to nonlinear elastic wave equations with viscoelastic terms in the framework of Lp-Sobolev spaces

Abstract

The Cauchy problem for nonlinear elastic wave equations with viscoelastic damping terms is investigated in the Lp framework. Sharp estimates of the global solutions in t for the higher order derivatives are established. The proof is based on the Gronwall type argument for 1<p<∞, the use of the difference of the propagation speed of the fundamental solutions for p=1 and the bootstrap argument for p=∞, combined with the sharp estimates for the linearized solutions.