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This article is cited in 3 scientific papers (total in 3 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
DOI:
https://doi.org/10.4213/faa3206
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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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http://mi.mathnet.ru/eng/faa3206https://doi.org/10.4213/faa3206 http://mi.mathnet.ru/eng/faa/v49/i4/p82
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This publication is cited in the following articles:
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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
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S. V. Zakharov, “Asymptotic solution of the multidimensional Burgers equation near a singularity”, Theoret. and Math. Phys., 196:1 (2018), 976–982
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Sergey V. Zakharov, “Asymptotic solutions of a parabolic equation near singular points of $A$ and $B$ types”, Ural Math. J., 5:1 (2019), 101–108
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