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Diffusion through thin layers with high specific heat. (English) Zbl 0724.35010

We study the asymptotic behaviour of the diffusion-transmission problem in a fixed domain surrounded by a layer whose thickness of order \(\delta\) goes to zero and where the specific heat \(\sigma\) goes to infinity. We characterize essentially three limit cases according to the limit \(\alpha\) of the product \(\delta\alpha\) : if \(\alpha =0\) or \(\alpha =\infty\) we have a Neumann or a Dirichlet boundary condition respectively, while if \(0<\alpha <\infty\) we obtain a mixed boundary condition involving the trace of the time derivative. We also extend this result to a class of unilateral problems of Signorini type.
Reviewer: Pierluigi Colli

MSC:

35B25 Singular perturbations in context of PDEs
35K05 Heat equation
35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
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