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On the destruction of ion-sound waves in plasma with strong space-time dispersion

Author: M. O. Korpusov
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 23 (2011), nomer 6.
Journal: St. Petersburg Math. J. 23 (2012), 989-1011
MSC (2010): Primary 35Q60
Published electronically: September 17, 2012
MathSciNet review: 2962182
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Abstract: The object of study in this paper is a model equation that describes ion-sound waves in plasma with the account of strong nonlinear dissipation and nonlinear sources of general type, together with strong space-time dispersion. Sufficient destruction conditions are obtained for the solution of the corresponding initial boundary problem in a bounded three-dimensional domain with homogeneous Dirichlet-Neumann conditions on the boundary. Moreover, the life-time of the solution is estimated. Finally, it is proved that, for every initial data in $ \mathbb{H}_0^2(\Omega )$, a strong generalized solution of this problem exists locally in time, i.e., it is shown that the solution destruction time is always positive.

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Additional Information

M. O. Korpusov
Affiliation: Department of Physics, Lomonosov Moscow State University, Moscow, Russia

Keywords: Destruction, equations of Sobolev type, nonlinear analysis
Received by editor(s): May 27, 2010
Published electronically: September 17, 2012
Additional Notes: Supported by RFBR, grant no. 11-01-12018-ofi-m-2011, and by the President program for the support of young doctors of science, MD-99.2009.1
Article copyright: © Copyright 2012 American Mathematical Society

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