This article is cited in 6 papers

On the blow-up of a solution of a non-local system of equations of hydrodynamic type

E. V. Yushkov

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

Abstract: We study Oskolkov's non-linear non-local system of equations with a source and the applicability of an operator method. We prove the existence of a weak solution of the initial-boundary value problem for this system and investigate uniqueness conditions for a weak solution. Sufficient conditions for the blow-up of a solution of the problem are found and upper and lower bounds are obtained for the time of blowing up of a solution. We also consider the smoothness problem for a weak solution.

Keywords: blow-up of a solution, system of hydrodynamic type, non-local initial-boundary value problem.

UDC: 517.957

MSC: Primary 35B44; Secondary 76E99

Received: 22.10.2010

DOI: 10.4213/im5556

 English version: Izvestiya: Mathematics, 2012, 76:1, 190–213

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