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2007, Volume 2007: 181-190. Doi: 10.3934/proc.2007.2007.181 open access
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Parabolic problems with varying operators and Dirichlet and Neumann boundary conditions on varying sets

  • 1.

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

  • 2.

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

Received:  August 31, 2006
Revised:  January 31, 2007
Published:  August 2007
Abstract Related Papers Cited by
    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.
    Mathematics Subject Classification: Primary: 35B40 Secondary: 35B27.

    Citation:
    shu

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