Uniform attractors for a semilinear evolution problem in hereditary simple fluids

Abstract

This paper is devoted to study the asymptotic behavior, as time tends to infinity, of the solutions of a semilinear partial differential equation of hyperbolic type with a convolution term describing simple fluids with fading memory. The past history of the displacement is regarded itself as a new variable, so that the corresponding initial boundary value problem is transformed into a dynamical system in a history space setting. Under proper assumptions on the nonlinear term, the existence of an uniform absorbing set and an universal attractor in suitable function spaces are achieved.