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Izvestiya: Mathematics, 2012, Volume 76, Issue 1, Pages 190–213
DOI: https://doi.org/10.1070/IM2012v076n01ABEH002580 (Mi im5556) 		 
This article is cited in 2 scientific papers (total in 2 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
English version PDF (310 kB) Citations (2) Russian version article
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DOI: https://doi.org/10.1070/IM2012v076n01ABEH002580
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.
Received: 22.10.2010
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: Primary 35B44; Secondary 76E99
Language: English
Original paper language: Russian
Citation: E. V. Yushkov, “On the blow-up of a solution of a non-local system of equations of hydrodynamic type”, Izv. Math., 76:1 (2012), 190–213
Citation in format AMSBIB
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\paper On the blow-up of a~solution of a~non-local system of equations of hydrodynamic type
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\yr 2012
\vol 76
\issue 1
\pages 190--213
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  • https://doi.org/10.1070/IM2012v076n01ABEH002580
  • https://www.mathnet.ru/eng/im/v76/i1/p201
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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