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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2013, Volume 10, Pages 311–323
(Mi semr415)
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This article is cited in 1 scientific paper (total in 1 paper)
Differentical equations, dynamical systems and optimal control
Dissipativity of boundary condition in a mixed problem for the three-dimensional wave equation
V. M. Gordienkoab a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Abstract:
We consider a mixed problem for the real three-dimensional wave equation satisfying the uniform Lopatinskii condition. We describe all feasible ways of reduction of the problem to the mixed problem for the symmetric hyperbolic system with the dissipative boundary condition. These ways are parametrized by points of the upper part of a four-dimensional bodily cone of the second order. We characterize the cone location and its geometric parameters by means of the coefficients of the boundary condition in the problem under consideration.
Keywords:
wave equation, mixed problem, symmetric hyperbolic system, dissipative boundary condition.
Received October 11, 2012, published April 10, 2013
Citation:
V. M. Gordienko, “Dissipativity of boundary condition in a mixed problem for the three-dimensional wave equation”, Sib. Èlektron. Mat. Izv., 10 (2013), 311–323
Linking options:
https://www.mathnet.ru/eng/semr415 https://www.mathnet.ru/eng/semr/v10/p311
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Abstract page: | 243 | Full-text PDF : | 74 | References: | 35 |
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