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Asymptotic problems connected with the heat equation in perforated domains. (English. Russian original) Zbl 0774.35028
Math. USSR, Sb. 71, No. 1, 125-147 (1992); translation from Mat. Sb. 181, No. 10, 1283-1305 (1990).
Summary: For the diffusion equation in the exterior of a closed set $$F\subset\mathbb{R}^ m$$, $$m\geq 2$$, with Neumann conditions on the boundary, $2\partial u/\partial t=\Delta u\quad\text{in }\mathbb{R}^ m\backslash F,\quad t>0,\quad \partial u/\partial n|_{\partial F}=0,\quad u|_{t=0}=f,$ pointwise stabilization, the central limit theorem, and uniform stabilization are studied. The basic condition on the set $$F$$ is formulated in terms of extension properties. Model examples of sets $$F$$ are indicated which are of interest from the viewpoint of mathematical physics and applied probability theory.

##### MSC:
 35K05 Heat equation 35B40 Asymptotic behavior of solutions to PDEs 76S05 Flows in porous media; filtration; seepage
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