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 $t\to\infty$ 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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