Nonlocal and nonlinear evolution equations in perforated domains
In this work we analyze the behavior of the solutions to nonlocal evolution equations of the form ut(x; t) = ∫ J(x - y)u(y; t) dy - h∑(x)u(x; t)+f(x; u(x; t)) with x in a perturbed domain Ω∑ C Ω which is thought as a fixed set Ω from where we remove a subset A∑ called the holes. We choose an appropr...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/135022 |
| Acceso en línea: | https://hdl.handle.net/11441/135022 https://doi.org/10.1016/j.jmaa.2020.124729 |
| Access Level: | acceso abierto |
| Palabra clave: | Perforated domains Nonlocal equations Semilinear equations Dirichlet problem Neumann problem |
| Sumario: | In this work we analyze the behavior of the solutions to nonlocal evolution equations of the form ut(x; t) = ∫ J(x - y)u(y; t) dy - h∑(x)u(x; t)+f(x; u(x; t)) with x in a perturbed domain Ω∑ C Ω which is thought as a fixed set Ω from where we remove a subset A∑ called the holes. We choose an appropriated families of functions h∑ € L∞ in order to deal with both Neumann and Dirichlet conditions in the holes setting a Dirichlet condition outside Ω. Moreover, we take J as a non-singular kernel and f as a nonlocal nonlinearity. Under the assumption that the characteristic functions of Ω€ have a weak limit, we study the limit of the solutions providing a nonlocal homogenized equation. |
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