Nonlocal and nonlinear evolution equations in perforated domains

Autor(es)

Pereira, Marcone C. ^[1] ; Sastre-Gomez, Silvia ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, IME, Dept Matemat Aplicada, Rua Matao 1010, Sao Paulo, SP - Brazil

^[2] Univ Nacl Educ Distancia, Dept Matemat Fundamentales, Calle Juan del Rosal 10, Madrid 28040 - Spain

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 495, n. 2 MAR 15 2021.
• Citações Web of Science: 0

Resumo

In this work we analyze the behavior of the solutions to nonlocal evolution equations of the form u(t) (x, t) = integral J(x - y)u(y, t) dy - h(epsilon)(x)u(x,t) f (x, u(x, t)) with x in a perturbed domain Omega(epsilon) subset of Omega which is thought as a fixed set Omega from where we remove a subset A(epsilon) called the holes. We choose appropriated families of functions h(epsilon) is an element of L-infinity in order to deal with both Neumann and Dirichlet conditions in the holes setting a Dirichlet condition outside Omega. Moreover, we take J as a non-singular kernel and f as a nonlocal nonlinearity. Under the assumption that the characteristic functions of Omega(epsilon) have a weak limit, we study the limit of the solutions providing a nonlocal homogenized equation. (C) 2020 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 17/02630-2 - Análise assintótica de equações diferenciais e integrais
• Beneficiário: Marcone Corrêa Pereira
• Modalidade de apoio: Auxílio à Pesquisa - Regular