Two-parameter asymptotics in the Cauchy problem for a quasi-linear parabolic equation

Article type: Research Article

Authors: Zakharov, Sergei V.

Affiliations: Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16, S. Kovalevskaja street, 620219, Ekaterinburg GSP-384, Russia

Note: [] Address for correspondence: Sergei V. Zakharov, 20-99, Krasnolesya street, 620016, Ekaterinburg, Russia. Tel.: +7 3433753462; E-mail: [email protected].

Abstract: The Cauchy problem for a quasi-linear parabolic equation with a small parameter ε at the higher derivative is considered. The derivative of the initial function is of order O(1/ρ), where ρ is another small parameter. We study the asymptotics of the solution of the problem in parameters ε and ρ tending to zero.

Keywords: Cauchy problem, two-parameter asymptotics

DOI: 10.3233/ASY-2008-0927

Journal: Asymptotic Analysis, vol. 63, no. 1-2, pp. 49-54, 2009