Existence, uniqueness and asymptotic behavior of solutions for a nonclassical diffusion equation with delay

Abstract

A nonclassical nonautonomous diffusion equation with delay is analyzed. First, we prove the existence and uniqueness of solutions by using the Galerkin approximations and the energy method. Next, we prove the existence and eventual uniqueness of stationary solutions, as well as their exponential stability. We emphasize that the assumptions imposed on the delay term include, in particular, the case of measurable variable delays.