American Institute of Mathematical Sciences

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2007, 2007(Special): 181-190. doi: 10.3934/proc.2007.2007.181

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

Carmen Calvo-Jurado 1, , Juan Casado-Díaz 2, and  Manuel Luna-Laynez 2,

1. 

Dpto. de Matemáticas. Escuela Politécnica., Avenida de la Universidad s/n., 10071 Cáceres, Spain
2. 

Dpto. de Ecuaciones Diferenciales y Análisis Numérico., Fac. de Matemáticas. C. Tarfia s/n., 41012 Sevilla, Spain, Spain

Received  September 2006 Revised  February 2007 Published  September 2007

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: parabolic problems, Homogenization, mixed boundary conditions..
Mathematics Subject Classification: Primary: 35B40 Secondary: 35B2.
Citation: Carmen Calvo-Jurado, Juan Casado-Díaz, Manuel Luna-Laynez. Parabolic problems with varying operators and Dirichlet and Neumann boundary conditions on varying sets. Conference Publications, 2007, 2007 (Special) : 181-190. doi: 10.3934/proc.2007.2007.181
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