Asymptotic analysis for a nonlinear viscoelastic problem with innite
history under a wider class of relaxation functions
Abstract
In this paper, we consider a nonlinear viscoelastic problem with
infinite history and a nonlinear feedback localized on the domain and a
relaxation function satisfying $$g^{\prime}(t)
\le -\xi(t)G(g(t)).$$ We establish
explicit and general decay rate results, using the multiplier method and
some properties of the convex functions. Our results are obtained
without imposing any restrictive growth assumption on the damping term
and without imposing any assumption on the boundedness of initial data
used in many earlier papers in the literature.