Materials with memory: an overview on admissible kernels in the integro- differential model equations

Materials with memory are modelled via integro-differential equations in which the integral term is introduced to take into account the past history of the material. The classical regularity requirements the kernel, which in viscoelasticity represents the relaxation function, is assumed to satisfy are considered. Aiming to model wider classes of materials, less restrictive as- sumptions are adopted. The results presented are part of a joint research program with M. Chipot, V. Valente and G. Vergara Caffarelli.