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Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 3, Pages 157–182 (Mi izv6330)  

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.

DOI: https://doi.org/10.4213/im6330

Full text: PDF file (602 kB)
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English version:
Izvestiya: Mathematics, 2012, 76:3, 581–606

Bibliographic databases:

UDC: 517.957
MSC: 35B44, 35D35, 35G61
Received: 08.12.2010

Citation: Yu. V. Mukhartova, A. A. Panin, “Blow-up of solutions of an inhomogeneous system of Sobolev-type equations”, Izv. RAN. Ser. Mat., 76:3 (2012), 157–182; Izv. Math., 76:3 (2012), 581–606

Citation in format AMSBIB
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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