A global existence theorem for the Dirichlet problem in nonlinear $n$-dimensional viscoelasticity

Abstract

We prove the existence and uniqueness of global smooth solutions to the Dirichlet initial-boundary problem in nonlinear $n$-dimensional viscoelasticity of integral type for small initial data in $H^{s_0}(\Omega)$, where $s_0$ is an integer smaller than that needed to establish the local existence. Moreover, the exponential decay of the solution is obtained.