Blow-up of solutions of an inhomogeneous system of Sobolev-type equations

Yu. V. Mukhartova, A. A. Panin

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: We consider a system of two inhomogeneous non-linear Sobolev-type equations of order 6 with second derivative with respect to the time variable. We prove that the problem is soluble locally in time, state sufficient conditions for blow-up of a solution at finite time, and give an upper bound for the blow-up time.

Keywords: blow-up, non-linear initial-boundary value problem, Sobolev-type equations.

UDC: 517.957

MSC: 35B44, 35D35, 35G61

Received: 08.12.2010

DOI: 10.4213/im6330

 English version: Izvestiya: Mathematics, 2012, 76:3, 581–606

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