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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 4, Pages 725–745 (Mi zvmmf4865)  
This article is cited in 2 scientific papers (total in 2 papers)

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

A. V. Kazeĭkina

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
Full-text PDF (334 kB) Citations (2)
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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 $t\to\infty$ 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.
Received: 26.11.2009
English version:
Computational Mathematics and Mathematical Physics, 2010, Volume 50, Issue 4, Pages 690–710
DOI: https://doi.org/10.1134/S0965542510040111
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: A. V. Kazeǐkina, “Stability of a traveling-wave solution of the Cauchy problem for the Korteweg–de Vries–Burgers equation”, Zh. Vychisl. Mat. Mat. Fiz., 50:4 (2010), 725–745; Comput. Math. Math. Phys., 50:4 (2010), 690–710
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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