Dynamics in dumbbell domains II. The limiting problem

Autor(es)

Arrieta, Jose M. ^[1] ; Carvalho, Alexandre N. ^[2] ; Lozada-Cruz, German ^[3]

Afiliação do(s) autor(es)

^[1] Univ Complutense Madrid, Dept Matemat Aplicada, Fac Matemat, E-28040 Madrid - Spain

^[2] Univ Sao Paulo, Dept Matemat, Inst Ciencias Matemat Computacao, BR-13560970 Sao Carlos, SP - Brazil

^[3] Univ Estadual Paulista, Dept Matemat, IBILCE, UNESP, BR-15054000 Sao Jose Dos Campos - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 247, n. 1, p. 174-202, JUL 1 2009.
• Citações Web of Science: 22

Resumo

In this work we continue the analysis of the asymptotic dynamics of reaction-diffusion problems in a dumbbell domain started in {[}J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2) (2006) 551-597]. Here we study the limiting problem, that is, an evolution problem in a ``domain{''} which consists of an open, bounded and smooth set Omega subset of R(N) with a curve R(0) attached to it. The evolution in both parts of the domain is governed by a parabolic equation. In Omega the evolution is independent of the evolution in R(0) whereas in R(0) the evolution depends on the evolution in Omega through the continuity condition of the solution at the junction points. We analyze in detail the linear elliptic and parabolic problem, the generation of linear and nonlinear semigroups, the existence and structure of attractors. (C) 2009 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 08/53094-4 - Sistemas dinâmicos em espaços de dimensão infinita sob perturbações
• Beneficiário: Alexandre Nolasco de Carvalho
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 07/00981-0 - Comportamento espectral de operadores em domínios tipo dumbbell
• Beneficiário: German Jesus Lozada Cruz
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 06/04781-3 - Dinâmica em domínios tipo Dumbbell: continuidade de atratores
• Beneficiário: German Jesus Lozada Cruz
• Modalidade de apoio: Auxílio à Pesquisa - Regular