On the upper semicontinuity of pullback attractors for multi-valued processes

Abstract

This paper is concerned with the asymptotical behavior of multi-valued processes. First, we establish some stability results of pullback attractors for multi-valued processes and display new methods to check the continuity condition. Then we consider the effects of small time delays on the asymptotic stability of multi-valued nonautonomous functional parabolic equations. Finally, we give some new estimates of solutions and prove the existence of minimal pullback attractors in H 0 1 ( Ω ) H_0^1(\Omega ) for nonautonomous nonclassical diffusion equations with polynomial growth nonlinearity of arbitrary order and without the uniqueness of solutions. In particular, the upper semicontinuity of pullback attractors for nonclassical diffusion equations with singular and nonautonomous perturbations is addressed.