Continuous Dependence on a Parameter of Exponential Attractors for Nonclassical Diffusion Equations

Abstract

In this paper, a new abstract result is given to verify the continuity of exponential attractors with respect to a parameter for the underlying semigroup. We do not impose any compact embedding on the main assumptions in the abstract result which is different from the corresponding result established by Efendiev et al. in 2004. Consequently, it can be used for equations whose solutions have no higher regularity. As an application, we prove the continuity of exponential attractors in H01 for a class of nonclassical diffusion equations with initial datum in H01.