A local/nonlocal diffusion model

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...

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Bibliographic Details
Published in:Applicable analysis 2022-10, Vol.101 (15), p.5213-5246
Main Authors: C. dos Santos, Bruna, Oliva, Sergio M., Rossi, Julio D.
Format: Article
Language:English
Subjects:
asymptotic behavior
Asymptotic properties
Diffusion
Domains
Evolution
Gradient flow
heat equation
Nonlocal diffusion
Thermodynamics
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Summary: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.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2021.1884227