`a`

Parabolic problems with varying operators and Dirichlet and Neumann boundary conditions on varying sets

Pages: 181 - 190, Issue Special, September 2007

 Abstract        Full Text (235.8K)              

Carmen Calvo-Jurado - Dpto. de Matemáticas. Escuela Politécnica., Avenida de la Universidad s/n., 10071 Cáceres, Spain (email)
Juan Casado-Díaz - Dpto. de Ecuaciones Diferenciales y Análisis Numérico., Fac. de Matemáticas. C. Tarfia s/n., 41012 Sevilla, Spain (email)
Manuel Luna-Laynez - Dpto. de Ecuaciones Diferenciales y Análisis Numérico., Fac. de Matemáticas. C. Tarfia s/n., 41012 Sevilla, Spain (email)

Abstract: For a bounded open set $\Omega$ $\subset$ $\mathbb{R}^N$ and an arbitrary sequence $\Gamma_n$ of closed subsets of $\partial\Omega$, we study the asymptotic behavior of the solutions of linear parabolic problems posed in $\Omega$ $\times$ (0, $T$) satisfying Dirichlet boundary conditions on $\Gamma_n$ $\times$ (0,T) and Neumman boundary conditions on ($\partial\Omega$ \ $\Gamma_n$) $\times$ (0, T). The coefficients of the equations are also assumed to vary with n. We obtain a limit problem which is stable by homogenization and where it appears a Fourier-Robin boundary condition.

Keywords:  Homogenization, parabolic problems, mixed boundary conditions.
Mathematics Subject Classification:  Primary: 35B40 Secondary: 35B27.

Received: September 2006;      Revised: February 2007;      Published: September 2007.