, Volume 50, Issue 4, pp 690-710
Date: 05 May 2010

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

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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).

Original Russian Text © A.V. Kazeykina, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 4, pp. 725–745.