This article is cited in 6 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.

UDC: 517.958

Received: 17.02.2014

DOI: 10.4213/faa3206

 English version: Functional Analysis and Its Applications, 2015, 49:4, 307–310

Bibliographic databases:

• 
• 
•