On the limit of solutions for a reaction-diffusion equation containing fractional Laplacians
A kind of nonlocal reaction-diffusion equations on an unbounded domain containing a fractional Laplacian operator is analyzed. To be precise, we prove the convergence of solutions of the equation governed by the fractional Laplacian to the solutions of the classical equation governed by the standard...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/156094 |
| Acceso en línea: | https://hdl.handle.net/11441/156094 https://doi.org/10.1007/s00245-023-10090-6 |
| Access Level: | acceso abierto |
| Palabra clave: | Fractional Laplacian Convergence of solutions Global attractors |
| Sumario: | A kind of nonlocal reaction-diffusion equations on an unbounded domain containing a fractional Laplacian operator is analyzed. To be precise, we prove the convergence of solutions of the equation governed by the fractional Laplacian to the solutions of the classical equation governed by the standard Laplacian, when the fractional parameter grows to 1. The existence of global attractors is investigated as well. The novelty of this paper is concerned with the convergence of solutions when the fractional parameter varies, which, as far as the authors are aware, seems to be the first result of this kind of problems in the literature. |
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