A local/nonlocal diffusion model
| Autor: | Julio D. Rossi, Sergio Muniz Oliva, Bruna C. dos Santos |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Coupling
Applied Mathematics 010102 general mathematics EQUAÇÕES DIFERENCIAIS PARCIAIS PARABÓLICAS 01 natural sciences 010101 applied mathematics Classical mechanics Mathematics - Analysis of PDEs FOS: Mathematics Heat equation 0101 mathematics Diffusion (business) Analysis Mathematics Analysis of PDEs (math.AP) |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| DOI: | 10.48550/arxiv.2003.02015 |
| Popis: | In this paper, we study some qualitative properties for an evolution problem that combines local and nonlocal diffusion operators acting in two different subdomains and, coupled in such a way that, the resulting evolution problem is the gradient flow of an energy functional. The coupling takes place at the interface between the regions in which the different diffusions take place. 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. Finally, we show a suitable way to recover the heat equation at the whole domain from taking the limit at the nonlocal rescaled kernel. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|