Large-time behavior for a fully nonlocal heat equation
We study the large-time behavior in all Lp norms and in different space-time scales of solutions to a nonlocal heat equation in RN involving a Caputo α-time derivative and a power of the Laplacian (− )s, s ∈ (0,1), extending recent results by the authors for the case s = 1. The initial data are assu...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/736720 |
| Acceso en línea: | https://hdl.handle.net/10486/736720 https://dx.doi.org/10.1007/s10013-020-00452-w |
| Access Level: | acceso abierto |
| Palabra clave: | Fully nonlocal heat equation caputo derivative fractional Laplacian asymptotic behavior Matemáticas |
| Sumario: | We study the large-time behavior in all Lp norms and in different space-time scales of solutions to a nonlocal heat equation in RN involving a Caputo α-time derivative and a power of the Laplacian (− )s, s ∈ (0,1), extending recent results by the authors for the case s = 1. The initial data are assumed to be integrable, and, when required, to be also in Lp. The main novelty with respect to the case s = 1 comes from the behaviour in fast scales, for which, thanks to the fat tails of the fundamental solution of the equation, we are able to give results that are not available neither for the case s = 1 nor, to our knowledge, for the standard heat equation, s = 1, α = 1 |
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