Global existence and energy decay of a nondissipative Cauchy viscoelastic problem

Abstract

A viscoelastic Cauchy problem subjected to a nonlinear source term is investigated. The memory term in the system involves a kernel which is regular, as is usually the case, but the system is not dissipative and is considered in the whole space. We prove global existence and nonexistence results. In the case of global existence, we show that solutions go to zero in a polynomial manner as time goes to infinity under some conditions on the source.