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Sbornik: Mathematics, 2006, Volume 197, Issue 6, Pages 835–851
DOI: https://doi.org/10.1070/SM2006v197n06ABEH003780 (Mi sm1574) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Asymptotic solution of a Cauchy problem in a neighbourhood of a gradient catastrophe

S. V. Zakharov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
English version PDF (305 kB) Citations (7)
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DOI: https://doi.org/10.1070/SM2006v197n06ABEH003780
Abstract: The existence of an asymptotic solution of a quasilinear parabolic equation with a small parameter is proved in a neighbourhood of the transition point of a weak discontinuity of the solution of the limiting equation into a shock wave. The behaviour of the first two coefficients of this asymptotic solution is studied in the entire plane of the stretched variables.
Bibliography: 4 titles.
Received: 16.12.2004
Russian version:
Matematicheskii Sbornik, 2006, Volume 197, Number 6, Pages 47–62
DOI: https://doi.org/10.4213/sm1574
Bibliographic databases:
UDC: 517.95
MSC: 35B40, 35K60
Language: English
Original paper language: Russian
Citation: S. V. Zakharov, “Asymptotic solution of a Cauchy problem in a neighbourhood of a gradient catastrophe”, Mat. Sb., 197:6 (2006), 47–62; Sb. Math., 197:6 (2006), 835–851
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2006v197n06ABEH003780
  • https://www.mathnet.ru/eng/sm/v197/i6/p47
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:363
    Russian version PDF:178
    English version PDF:15
    References:54
    First page:1
     
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