Nonlocal diffusion equations with dynamical boundary conditions. (June 2020)

• Record Type: Journal Article
• Authors: Berná, Pablo M.; Rossi, Julio D.
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 45G10 -- 45J05 -- 47H06; Nonlocal diffusion -- p-Laplacian -- Dynamical boundary conditions -- Accretive operators; 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.2020.111751
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study nonlocal problems that are analogous to the local ones given by the Laplacian or the p − Laplacian with dynamical boundary conditions. We deal both with smooth and with singular kernels and show existence and uniqueness of solutions and study their asymptotic behaviour as t goes to infinity.