Global existence, asymptotic behavior, and uniform attractor for a nonautonomous equation

Abstract

In this paper, we establish the global existence, asymptotic behavior, and uniform attractor for a nonautonomous viscoelastic equation with a delay term. Under some suitable assumptions, we firstly prove the global well‐posedness of the problem by using the Faedo–Galerkin approximations together with some energy estimates and then obtain the general decay results of the energy via suitable Lyapunov functionals. Finally, we prove the existence of uniform attractors. Copyright © 2013 John Wiley & Sons, Ltd.