Spatial homogeneity in parabolic problems with nonlinear boundary conditions

Alexandre Nolasco de Carvalho; Marcos Roberto Teixeira Primo

doi:10.3934/cpaa.2004.3.637

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2004, Volume 3, Issue 4: 637-651. Doi: 10.3934/cpaa.2004.3.637

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Spatial homogeneity in parabolic problems with nonlinear boundary conditions

1.
Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Caixa postal 668, 13560-970 São Carlos, São Paulo
2.
Departamento de Matemática, Universidade Estadual de Maringá, 87020-900 Maringá, Paraná

Received: October 2003

Revised: May 2004

Published: December 2004

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Abstract

In this work we prove that global attractors of systems of weakly coupled parabolic equations with nonlinear boundary conditions and large diffusivity are close to attractors of an ordinary differential equation. The limiting ordinary differential equation is given explicitly in terms of the reaction, boundary flux, the $n$-dimensional Lebesgue measure of the domain and the $(n-1)-$Hausdorff measure of its boundary. The tools are invariant manifold theory and comparison results.

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Mathematics Subject Classification: 34D35, 34D45, 35B05, 35B40, 35K40.

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