ASYMPTOTIC SOLUTIONS OF A PARABOLIC EQUATION NEAR SINGULAR POINTS OF \(A\) AND \(B\) TYPES

ASYMPTOTIC SOLUTIONS OF A PARABOLIC EQUATION NEAR SINGULAR POINTS OF \(A\) AND \(B\) TYPES

The Cauchy problem for a quasi-linear parabolic equation with a small parameter multiplying a higher derivative is considered in two cases when the solution of the limit problem has a point of gradient catastrophe. Asymptotic solutions are found by using the Cole–Hopf transform. The integrals determ...

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Bibliographic Details
Main Author: Sergey V. Zakharov
Format: Article
Language:English
Published: Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics 2019-07-01
Series:Ural Mathematical Journal
Subjects:
Quasi-linear parabolic equation, Cole–Hopf transform, Singular points, Asymptotic solutions, Whitney fold singularity, Il'in's universal solution, Weighted Sobolev spaces
Online Access:https://umjuran.ru/index.php/umj/article/view/145
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