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Izvestiya: Mathematics, 2014, Volume 78, Issue 5, Pages 937–985
DOI: https://doi.org/10.1070/IM2014v078n05ABEH002714 (Mi im8118) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Blow-up of solutions of an abstract Cauchy problem for a formally hyperbolic equation with double non-linearity

M. O. Korpusov, A. A. Panin

M. V. Lomonosov Moscow State University, Faculty of Physics
English version PDF (519 kB) Citations (8)
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DOI: https://doi.org/10.1070/IM2014v078n05ABEH002714
Abstract: We consider an abstract Cauchy problem for a formally hyperbolic equation with double non-linearity. Under certain conditions on the operators in the equation, we prove its local (in time) solubility and give sufficient conditions for finite-time blow-up of solutions of the corresponding abstract Cauchy problem. The proof uses a modification of a method of Levine. We give examples of Cauchy problems and initial-boundary value problems for concrete non-linear equations of mathematical physics.
Keywords: finite-time blow-up, generalized Klein–Gordon equations, non-linear hyperbolic equations, non-linear mixed boundary-value problems, field theory.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-12018-офи-м
Received: 17.03.2013
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2014, Volume 78, Issue 5, Pages 91–142
DOI: https://doi.org/10.4213/im8118
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: 35B44, 35L20, 35L70
Language: English
Original paper language: Russian
Citation: M. O. Korpusov, A. A. Panin, “Blow-up of solutions of an abstract Cauchy problem for a formally hyperbolic equation with double non-linearity”, Izv. Math., 78:5 (2014), 937–985
Citation in format AMSBIB
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\by M.~O.~Korpusov, A.~A.~Panin
\paper Blow-up of solutions of an abstract Cauchy problem for a~formally hyperbolic equation with double non-linearity
\jour Izv. Math.
\yr 2014
\vol 78
\issue 5
\pages 937--985
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\crossref{https://doi.org/10.1070/IM2014v078n05ABEH002714}
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  • https://doi.org/10.1070/IM2014v078n05ABEH002714
  • https://www.mathnet.ru/eng/im/v78/i5/p91
    • This publication is cited in the following 8 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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    Abstract page:681
    Russian version PDF:223
    English version PDF:19
    References:88
    First page:29
     
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