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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 1990 Volume 181, Number 10, Pages 1283–1305 (Mi sm1225)

This article is cited in 15 papers

Asymptotic problems connected with the heat equation in perforated domains

V. V. Zhikov


Abstract: For the diffusion equation in the exterior of a closed set $F\subset\mathbf R^m$, $m\geqslant 2$, with Neumann conditions on the boundary,
\begin{gather*} 2\frac{\partial u}{\partial t}=\nabla u \quad\text{in}\quad \mathbf R^m\setminus F, \quad t>0, \\ \frac{\partial u}{\partial n}\bigg|_{\partial F}=0, \quad u\big|_{t=0}=f, \end{gather*}
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.

UDC: 517.9

MSC: Primary 35K05, 35B40; Secondary 76S05

Received: 10.01.1990


 English version:
Mathematics of the USSR-Sbornik, 1992, 71:1, 125–147

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