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Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 4, Pages 82–85 (Mi faa3206)  

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

Brief communications

Singularities of $A$ and $B$ Types in Asymptotic Analysis of Solutions of a Parabolic Equation

S. V. Zakharov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: The Cauchy problem for a quasi-linear parabolic equation with a small parameter multiplying a higher derivative is considered in two cases where the solution of the limit problem has a point of gradient catastrophe. The integrals determining the leading approximation correspond to the Lagrange singularity of type $A_3$ and the boundary singularity of type $B_3$. For another choice of the initial function, singular points corresponding to $A_{2n+1}$ and $B_{2n+1}$ with arbitrary $n\ge 1$ are obtained.

Keywords: parabolic equation, asymptotics, singular points

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00322
Russian Academy of Sciences - Federal Agency for Scientific Organizations


DOI: https://doi.org/10.4213/faa3206

Full text: PDF file (142 kB)
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English version:
Functional Analysis and Its Applications, 2015, 49:4, 307–310

Bibliographic databases:

UDC: 517.958
Received: 17.02.2014

Citation: S. V. Zakharov, “Singularities of $A$ and $B$ Types in Asymptotic Analysis of Solutions of a Parabolic Equation”, Funktsional. Anal. i Prilozhen., 49:4 (2015), 82–85; Funct. Anal. Appl., 49:4 (2015), 307–310

Citation in format AMSBIB
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\paper Singularities of~$A$ and~$B$ Types in Asymptotic Analysis of Solutions of a Parabolic Equation
\jour Funktsional. Anal. i Prilozhen.
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\pages 82--85
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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. 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
    2. S. V. Zakharov, “Asymptotic solution of the multidimensional Burgers equation near a singularity”, Theoret. and Math. Phys., 196:1 (2018), 976–982  mathnet  crossref  crossref  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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