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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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