Regularity theory for a nonlinear fractional reaction–diffusion equation. (June 2020)

• Record Type: Journal Article
• Authors: de Andrade, Bruno; Cruz, Thamires Santos
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: primary 35K57, 45K05 -- secondary 35R11; Fractional diffusion equations -- Regularity theory of solutions -- Blow-up alternative; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111705
• Languages: English
• ISSNs: 0362-546X

Abstract

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.