Asymptotic behaviour in linear viscoelasticity

Abstract

We study the asymptotic behaviour of the solution of the viscoelastic equation, and we prove for a bounded domain that the energy associated to this system approaches zero exponentially as time goes to infinity. Moreover, for the whole space R n {\mathbb {R}^n} we will prove that the displacement vector field can be decomposed into two parts, solenoidal and irrotational, whose corresponding energies decay to zero uniformly as time goes to infinity with rates that depend on the regularity of the initial data.