Regularity theory for a nonlinear fractional reaction–diffusion equation. (June 2020) - de Andrade, Bruno; Cruz, Thamires Santos
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 L q setting. Furthermore, we consider global existence or non-continuation by a blow-up of such solutions.