Abstract Volterra integrodifferential equations with applications to parabolic models with memory

Abstract

In this paper we are concerned with local existence, regularity and continuous dependence upon the initial data of ϵ-regular mild solutions for the abstract integrodifferential equation (1, 2). We also present a result on unique continuation and a blow-up alternative for an ϵ-regular mild solution of (1, 2). Finally, we apply our results to three interesting models: Navier–Stokes equations with memory, diffusion equations with memory and a strongly damped plate equation with memory.