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

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  • 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.

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