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

Korpusov, M.

doi:10.1090/S1061-0022-2012-01226-4

On the destruction of ion-sound waves in plasma with strong space-time dispersion
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by M. O. Korpusov
Translated by: S. V. Kislyakov

St. Petersburg Math. J. 23 (2012), 989-1011

DOI: https://doi.org/10.1090/S1061-0022-2012-01226-4

Published electronically: September 17, 2012

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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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