A local/nonlocal diffusion model. Issue 15 (13th October 2022)

• Record Type: Journal Article
• Authors: C. dos Santos, Bruna; Oliva, Sergio M.; Rossi, Julio D.
• Is Part Of: Applicable analysis. Volume 101:Issue 15(2022)
• Page Start: 5213
• Page End: 5246
• Publication Date: 2022-10-13
• Subjects: Nonlocal diffusion -- heat equation -- asymptotic behavior; 35K55 -- 35B40 -- 35A05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1884227
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we study some qualitative properties for solutions to an evolution problem that combines local and nonlocal diffusion operators acting in two different subdomains. The coupling takes place at the interface between these two domains in such a way that the resulting evolution problem is the gradient flow of an energy functional. We prove existence and uniqueness results, as well as that the model preserves the total mass of the initial condition. We also study the asymptotic behavior of the solutions. Besides, we show a suitable way to recover the heat equation at the whole domain from taking the limit at the nonlocal rescaled kernel. Finally, we propose a brief discussion about the extension of the problem to higher dimensions.