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Stability of a traveling-wave solution to the Cauchy problem for the Korteweg-de Vries-Burgers equation

  • A. V. KazeykinaEmail author
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Abstract

The asymptotic behavior of the solution to the Cauchy problem for the Korteweg-de Vries-Burgers equation u t + (f(u)) x + au xxx bu xx = 0 as t → ∞ is analyzed. Sufficient conditions for the existence and local stability of a traveling-wave solution known in the case of f(u) = u 2 are extended to the case of an arbitrary sufficiently smooth convex function f(u).

Key words

Korteweg-de Vries-Burgers equation traveling-wave solution asymptotic behavior of the Cauchy problem solution 

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia

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