Patterns in parabolic problems with nonlinear boundary conditions


Autoria(s): Carvalho, Alexandre Nolasco de; Cruz, German Jesus Lozada
Contribuinte(s)

Universidade Estadual Paulista (UNESP)

Data(s)

20/05/2014

20/05/2014

15/01/2007

Resumo

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Processo FAPESP: 2003/10042-0

Processo FAPESP: 2000/01479-8

We obtain existence of asymptotically stable nonconstant equilibrium solutions for semilinear parabolic equations with nonlinear boundary conditions on small domains connected by thin channels. We prove the convergence of eigenvalues and eigenfunctions of the Laplace operator in such domains. This information is used to show that the asymptotic dynamics of the heat equation in this domain is equivalent to the asymptotic dynamics of a system of two ordinary differential equations diffusively (weakly) coupled. The main tools employed are the invariant manifold theory and a uniform trace theorem. (c) 2006 Elsevier B.V. All rights reserved.

Formato

1216-1239

Identificador

http://dx.doi.org/10.1016/j.jmaa.2006.02.046

Journal of Mathematical Analysis and Applications. San Diego: Academic Press Inc. Elsevier B.V., v. 325, n. 2, p. 1216-1239, 2007.

0022-247X

http://hdl.handle.net/11449/32922

10.1016/j.jmaa.2006.02.046

WOS:000242730600032

WOS000242730600032.pdf

Idioma(s)

eng

Publicador

Elsevier B.V.

Relação

Journal of Mathematical Analysis and Applications

Direitos

openAccess

Palavras-Chave #Semilinear parabolic problems #Nonlinear boundary conditions #Dumbbell domains #Stable nonconstant equilibria #Invariant manifolds
Tipo

info:eu-repo/semantics/article