Abstract
The asymptotic behavior of the solution to the Cauchy problem for the Korteweg-de Vries-Burgers equation ut + (f(u))x + auxxx − buxx = 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) = u2 are extended to the case of an arbitrary sufficiently smooth convex function f(u).
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