This article is cited in 12 papers

On the Nonextendable Solution and Blow-Up of the Solution of the One-Dimensional Equation of Ion-Sound Waves in a Plasma

M. O. Korpusov^a, A. A. Panin<sup>ab

a</sup> Lomonosov Moscow State University
^b Peoples Friendship University of Russia, Moscow

Abstract: The initial boundary-value problem for the equation of ion-sound waves in a plasma is studied. A theorem on the nonextendable solution is proved. Sufficient conditions for the blow-up of the solution in finite time and the upper bound for the blow-up time are obtained using the method of test functions.

Keywords: blow-up of the solution, nonlinear initial boundary-value problem, Sobolev-type equation, exponential nonlinearity.

UDC: 517.957

Received: 14.09.2016

DOI: 10.4213/mzm11377

 English version: Mathematical Notes, 2017, 102:3, 350–360

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