Spatial homogeneity in parabolic problems with nonlinear boundary conditions

Alexandre Nolasco de Carvalho; Marcos Roberto Teixeira Primo

doi:10.3934/cpaa.2004.3.637

Article Contents

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

This issue Previous Article Persistent regional null contrillability for a class of degenerate parabolic equations Next Article Uniqueness and boundary behavior of large solutions to elliptic problems with singular weights

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: September 30, 2003

Revised: April 30, 2004

Published: November 2004

Abstract Related Papers Cited by

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.

Keywords:

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

Citation:

Article Metrics

HTML views() PDF downloads(94) Cited by(0)

Spatial homogeneity in parabolic problems with nonlinear boundary conditions

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Spatial homogeneity in parabolic problems with nonlinear boundary conditions

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content