Unité Mixte de Recherche du C.N.R.S. N°7534

Abstract : Using the unfolding method of Cioranescu, Damlamian and Griso (CRAS, 2002), we study the homogenization for equations of the form $-\Div d_\epsilon=f$, with $(\nabla u_\epsilon(x),d_\epsilon(x)) \in A_\epsilon(x)$ and where $A_\epsilon$ is a function whose values are maximal monotone graphs. Under appropriate growth and coercivity assumptions, if the sequence of unfolded maximal monotone graphs $(\mathcal{T}_\epsilon (A_\epsilon ))(x,y)$ converges in the graphical sense to a maximal monotone graph $B(x,y)$ for almost every $(x,y)\in \Omega \times Y$, as $\epsilon \to 0$, then $(u_\epsilon , d_\epsilon )$ converges weakly in a suitable Sobolev space to a solution $(u_0,d_0)$ of the problem $-\Div d_0=f$, with $(\nabla u_0(x),d_0(x)) \in A(x)$ and $A$ satisfies the same assumptions as $A_\epsilon$. This result includes the case where $A_\epsilon(x)$ is a monotone continuous function for almost every $x$ in $\Omega$.

 Periodic homogenization of monotone multivalued operators
 DAMLAMIAN Alain, MEUNIER Nicolas, VAN SCHAFTINGEN Jean
2006-12
24-02-2006

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