Coupled local/nonlocal models in thin domains

Article type: Research Article

Authors: dos Santos, Bruna C.^a | Oliva, Sergio M.^a | Rossi, Julio D.^{b; *}

Affiliations: [a] IME-USP, Institute of Mathematics and Statistics, University of São Paulo, Brazil | [b] Department of Mathematics, FCEyN, University of Buenos Aires, Argentina

Correspondence: [*] Corresponding author. E-mail: jrossi@dm.uba.ar.

Abstract: In this paper, we analyze a model composed by coupled local and nonlocal diffusion equations acting in different subdomains. We consider the limit case when one of the subdomains is thin in one direction (it is concentrated to a domain of smaller dimension) and as a limit problem we obtain coupling between local and nonlocal equations acting in domains of different dimension. We find existence and uniqueness of solutions and we prove several qualitative properties (like conservation of mass and convergence to the mean value of the initial condition as time goes to infinity).

Keywords: Nonlocal diffusion, heat equation, asymptotic behavior

DOI: 10.3233/ASY-211740

Journal: Asymptotic Analysis, vol. 129, no. 3-4, pp. 545-575, 2022