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This article is cited in 15 scientific papers (total 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.
Received: 10.01.1990
Citation:
V. V. Zhikov, “Asymptotic problems connected with the heat equation in perforated domains”, Math. USSR-Sb., 71:1 (1992), 125–147
Linking options:
https://www.mathnet.ru/eng/sm1225https://doi.org/10.1070/SM1992v071n01ABEH002128 https://www.mathnet.ru/eng/sm/v181/i10/p1283
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Abstract page: | 613 | Russian version PDF: | 171 | English version PDF: | 19 | References: | 67 | First page: | 1 |
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