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On stabilization of the solution of the third mixed problem for the wave equation in a cylindrical domain
V. M. Favorin
Abstract:
Necessary and sufficient conditions are obtained for stabilization as $t\to\infty$ of the solution of the third mixed problem for the wave equation in the exterior of an infinite closed cylindrical surface in space variables, in the presence of an influx of energy into the region through the boundary $\bigl(\frac{\partial u}{\partial n}+g(x)u|_{\partial\Omega}=0$, $g(x)$ of arbitrary sign$\bigr)$. An asymptotic expansion as $t\to\infty$ is established for the solution.
Bibliography: 18 titles.
Received: 09.11.1982
Citation:
V. M. Favorin, “On stabilization of the solution of the third mixed problem for the wave equation in a cylindrical domain”, Math. USSR-Sb., 51:2 (1985), 287–314
Linking options:
https://www.mathnet.ru/eng/sm2023https://doi.org/10.1070/SM1985v051n02ABEH002861 https://www.mathnet.ru/eng/sm/v165/i3/p291
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Abstract page: | 405 | Russian version PDF: | 104 | English version PDF: | 22 | References: | 76 |
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