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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 7, Pages 1170–1175 (Mi zvmmf10589)  

This article is cited in 2 scientific papers (total in 2 papers)

Instantaneous blow-up of classical solutions to the Cauchy problem for the Khokhlov–Zabolotskaya equation

M. O. Korpusov, S. G. Mikhailenko

Faculty of Physics, Moscow State University, Moscow, Russia

Abstract: The Cauchy problem for a second-order nonlinear equation with mixed derivatives is considered. It is proved that its classical local-in-time solution does not exist. The blow-up of the solution is proved by applying S. I. Pohozaev and E. L. Mitidieri's nonlinear capacity method.

Key words: nonlinear capacity, blow-up.

DOI: https://doi.org/10.7868/S0044466917030097

Full text: PDF file (117 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:7, 1167–1172

Bibliographic databases:

UDC: 519.634
Received: 28.10.2015

Citation: M. O. Korpusov, S. G. Mikhailenko, “Instantaneous blow-up of classical solutions to the Cauchy problem for the Khokhlov–Zabolotskaya equation”, Zh. Vychisl. Mat. Mat. Fiz., 57:7 (2017), 1170–1175; Comput. Math. Math. Phys., 57:7 (2017), 1167–1172

Citation in format AMSBIB
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\by M.~O.~Korpusov, S.~G.~Mikhailenko
\paper Instantaneous blow-up of classical solutions to the Cauchy problem for the Khokhlov--Zabolotskaya equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2017
\vol 57
\issue 7
\pages 1170--1175
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\crossref{https://doi.org/10.7868/S0044466917030097}
\elib{https://elibrary.ru/item.asp?id=29404224}
\transl
\jour Comput. Math. Math. Phys.
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\vol 57
\issue 7
\pages 1167--1172
\crossref{https://doi.org/10.1134/S0965542517030095}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85026823107}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. O. Korpusov, “Solution blowup for nonlinear equations of the Khokhlov–Zabolotskaya type”, Theoret. and Math. Phys., 194:3 (2018), 347–359  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. Korpusov M.O., “Instantaneous Blow-Up of a Weak Solution of a Problem in Plasma Theory on the Half-Line”, Differ. Equ., 55:1 (2019), 60–67  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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