Homogenization of nonlinear parabolic problems with varying boundary conditions on varying sets

Abstract

This paper reports on a study of the asymptotic behaviour of the solution of a nonlinear parabolic problem posed on a sequence of varying domains. We also consider that the solution satisfies a Neumann boundary condition on an arbitrary sequence of subsets of the boundary and a Dirichlet boundary condition on the remainder of it. Assuming that the operators do not depend on time, we show that the corrector obtained for the elliptic problem, still gives a corrector for the parabolic problem. From this result, we obtain the limit problem which is stable by homogenization and where it appears, a generalized Fourier boundary condition.

Keywords:

• Homogenization
• Varying domains
• Nonlinear parabolic problems
• Varying boundary conditions

Acknowledgements

This work has been partly supported by the project BFM2002-00672 of the Ministerio de Ciencia y Tecnolog´ia.

Additional information

Notes on contributors

Carmen Calvo-Jurado

Email: [email protected]