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Étude de la conduction stationnaire dans un domaine comportant une répartition périodique d’inclusions minces de grande conductivité. (French) Zbl 0587.35041

We study the stationary heat equation in a domain which comprises an \(\epsilon\) Y-periodic distribution of thin inclusions of thickness \(e\epsilon\). The limits (e\(\to 0\) then \(\epsilon\) \(\to 0)\), (\(\epsilon\) \(\to 0\) then \(e\to 0)\) and lastly (e\(\to 0\) and \(\epsilon\) \(\to 0\) together) give the same result; this shows that the relative order of magnitude between the two small parameters is without any influence upon the limit-behaviour.

MSC:

35K05 Heat equation
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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References:

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