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) =
R
J(x�����y)u(y; t) dy �����h"(x)u(x; t)+f(x; u(x; t)) with x in a
perturbed domain
"
which is thought ... In this work we analyze the behavior of the solutions to nonlocal evolution equations of the form ut(x; t) = R J(x�����y)u(y; t) dy �����h"(x)u(x; t)+f(x; u(x; t)) with x in a perturbed domain " which is thought as a xed set from where we remove a subset A" called the holes. We choose an appropriated families of functions h" 2 L1 in order to deal with both Neumann and Dirichlet conditions in the holes setting a Dirichlet condition outside . Moreover, we take J as a non-singular kernel and f as a nonlocal nonlinearity. Under the assumption that the characteristic functions of " 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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