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Mat. Sb., 2006, Volume 197, Number 6, Pages 47–62 (Mi msb1574)  

This article is cited in 4 scientific papers (total in 4 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

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.

DOI: https://doi.org/10.4213/sm1574

Full text: PDF file (495 kB)
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English version:
Sbornik: Mathematics, 2006, 197:6, 835–851

Bibliographic databases:

UDC: 517.95
MSC: 35B40, 35K60
Received: 16.12.2004

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Zakharov, “A construction of a solution to the Burgers equation with a specified asymptotics”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S243–S249  mathnet  crossref  elib
    2. S. V. Zakharov, “Singulyarnye asimptotiki v zadache Koshi dlya parabolicheskogo uravneniya s malym parametrom”, Tr. IMM UrO RAN, 21, no. 1, 2015, 97–104  mathnet  mathscinet  elib
    3. S. V. Zakharov, “Singularities of $A$ and $B$ Types in Asymptotic Analysis of Solutions of a Parabolic Equation”, Funct. Anal. Appl., 49:4 (2015), 307–310  mathnet  crossref  crossref  isi  elib
    4. A. R. Danilin, S. V. Zakharov, O. O. Kovrizhnykh, E. F. Lelikova, I. V. Pershin, O. Yu. Khachai, “Ekaterinburgskoe nasledie Arlena Mikhailovicha Ilina”, Tr. IMM UrO RAN, 23, no. 2, 2017, 42–66  mathnet  crossref  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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