This article is cited in 5 papers

Asymptotic solution of the multidimensional Burgers equation near a singularity

S. V. Zakharov

Krasovskii Institute for Mathematics and Mechanics, Ural Branch, RAS, Ekaterinenburg, Russia

Abstract: We consider the Cauchy problem for the multidimensional Burgers equation with a small dissipation parameter and use the matching method to construct an asymptotic solution near the singularity determined by the vector field structure at the initial instant. The method that we use allows tracing the evolution of the solution with a hierarchy of differently scaled structures and giving a rigorous mathematical definition of the asymptotic solution in the leading approximation. We discuss the relation of the considered problem to different models in fundamental and applied physics.

Keywords: multidimensional Burgers equation, Cauchy problem, asymptotics.

Received: 09.10.2017
Revised: 23.01.2018

DOI: 10.4213/tmf9479

 English version: Theoretical and Mathematical Physics, 2018, 196:1, 976–982

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