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

摘要

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.