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Analysis reveals asymptotic behavior of renormalized solutions in porous media, highlighting Robin-type boundary conditions.
We consider a class of quasilinear elliptic problems with L1 data, set in a domain periodically perforated by two kinds of holes. A Robin-type condition depending on a parameter γ is imposed on the boundary of some holes, while a Dirichlet condition is prescribed on the boundary of the remaining holes as well as on the external boundary of the domain. Our goal is to describe the asymptotic behavior of the renormalized solution of this problem, given that the solution does not belong to H1 and to derive the corresponding limit problem.
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Karek et al. (2025) studied this question.
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