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Sbornik: Mathematics, 2001, Volume 192, Issue 10, Pages 1417–1433
DOI: https://doi.org/10.1070/SM2001v192n10ABEH000599 (Mi sm599) 		 
This article is cited in 23 scientific papers (total in 24 papers)

From weak discontinuity to gradient catastrophe

S. V. Zakharov, A. M. Il'in

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
English version PDF (204 kB) Citations (24)
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DOI: https://doi.org/10.1070/SM2001v192n10ABEH000599
Abstract: The Cauchy problem for a quasilinear parabolic equation with small parameter at the highest derivative is considered in the case when the solution of the degenerate equation has a weak discontinuity subsequently turning into a strong discontinuity. The singularities that the coefficients of the asymptotic formula representing the solution in the boundary layer of the weak discontinuity develop on approaching the point of the gradient catastrophe are analysed.
Received: 25.01.2001
Russian version:
Matematicheskii Sbornik, 2001, Volume 192, Number 10, Pages 3–18
DOI: https://doi.org/10.4213/sm599
Bibliographic databases:
UDC: 517.95
MSC: Primary 35B40, 35C20; Secondary 35K55
Language: English
Original paper language: Russian
Citation: S. V. Zakharov, A. M. Il'in, “From weak discontinuity to gradient catastrophe”, Mat. Sb., 192:10 (2001), 3–18; Sb. Math., 192:10 (2001), 1417–1433
Citation in format AMSBIB
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    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник - 1992–2005 Sbornik: Mathematics
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    English version PDF:9
    References:78
    First page:3
     
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