Spatial homogeneity in parabolic problems with nonlinear boundary conditions

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December 2004, 3(4): 637-651. doi: 10.3934/cpaa.2004.3.637

Spatial homogeneity in parabolic problems with nonlinear boundary conditions

Alexandre Nolasco de Carvalho ^1, and Marcos Roberto Teixeira Primo ^2,

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

Received October 2003 Revised May 2004 Published September 2004

Abstract
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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.

Keywords: comparison and positivity results, spatial homogeneity, Invariant manifold theory, global attractors.

Mathematics Subject Classification: 34D35, 34D45, 35B05, 35B40, 35K4.

Citation: Alexandre Nolasco de Carvalho, Marcos Roberto Teixeira Primo. Spatial homogeneity in parabolic problems with nonlinear boundary conditions. Communications on Pure & Applied Analysis, 2004, 3 (4) : 637-651. doi: 10.3934/cpaa.2004.3.637

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