Zhikov, V. V. 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. Cited in 3 Documents MSC: 35K05 Heat equation 35B40 Asymptotic behavior of solutions to PDEs 76S05 Flows in porous media; filtration; seepage Keywords:diffusion equation; Neumann conditions; pointwise stabilization; central limit theorem; uniform stabilization PDF BibTeX XML Cite \textit{V. V. Zhikov}, Math. USSR, Sb. 71, No. 1, 125--147 (1992; Zbl 0774.35028); translation from Mat. Sb. 181, No. 10, 1283--1305 (1990) Full Text: DOI