A remark on nonclassical diffusion equations with memory (Q253071)

The existence of regular exponential attractors for nonclassical diffusion equations with hereditary memory is investigated. The theory of semigroups is used to solve this problem. This integrodifferential problem is translated into a dynamical system within the past history framework. The problem both in the classical past history framework and in the minimal state framework is analyzed. The scheme of Dafermos and energy estimates are used for the researching problem in the classical past history framework. For the investigation problem in the minimal state framework the scheme developed by \textit{M. Fabrizio} et al. [Arch. Ration. Mech. Anal. 198, No. 1, 189--232 (2010; Zbl 1245.45010)] and energy estimates are used.