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

  • Authors:

  • Carmen Calvo-Jurado

  • Affiliations:

  • Departamento de Matemáticas, Universidad de Extremadura, Escuela Politécnica, Cáceres, Spain

  • Venue:
  • International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
  • Year:
  • 2008

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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.