Artículo
Nonlocal and nonlinear evolution equations in perforated domains
Autor/es | Corrêa Pereira, Marcone
Sastre Gómez, Silvia ![]() ![]() ![]() ![]() ![]() ![]() |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2020-12-02 |
Fecha de depósito | 2022-07-06 |
Publicado en |
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Resumen | 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 ... 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. |
Cita | Corrêa Pereira, M. y Sastre Gómez, S. (2020). Nonlocal and nonlinear evolution equations in perforated domains. Journal of Mathematical Analysis and Applications, 495 (2), 124729-1-124729-20. |
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