Regularity theory for a nonlinear fractional reaction–diffusion equation

Abstract

This paper is dedicated to the study of a nonlinear fractional reaction–diffusion equation. We analyze the behavior of the resolvent family associated with the problem in the scale of fractional power spaces associated with the Laplace operator. We ensure the existence and uniqueness of regular mild solutions to the problem in the Lq setting. Furthermore, we consider global existence or non-continuation by a blow-up of such solutions.