This article is cited in 2 papers

Blow-Up of the Solution of an Inhomogeneous System of Sobolev-Type Equations

Yu. V. Mukhartova, A. A. Panin

M. V. Lomonosov Moscow State University

Abstract: We consider a model system of two inhomogeneous nonlinear Sobolev-type equations of sixth order with second-order time derivative and prove the local (with respect to time) solvability of the problem. We state conditions under which the blow-up of the solution occurs in finite time and find an upper bound for the blow-up time.

Keywords: system of Sobolev-type equations, blow-up of solutions, blow-up time, ion-sound wave, locally Lipschitz operator, Banach space, Friedrichs inequality.

UDC: 519.17:5+514.113.4

Received: 25.05.2010
Revised: 22.11.2010

DOI: 10.4213/mzm9307

 English version: Mathematical Notes, 2012, 91:2, 217–230

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