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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2019, Volume 12, Issue 2, Pages 37–46
DOI: https://doi.org/10.14529/mmp190203
(Mi vyuru486)
 

Mathematical Modelling

On a nonlinear problem of the breaking water waves

M. Kiranea, B. T. Torebekbc

a Université de La Rochelle, La Rochelle, France
b Al-Farabi Kazakh National University, Almaty, Kazakhstan
c Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
References:
Abstract: The paper is devoted to the initial boundary value problem for the Korteweg-de Vries–Benjamin–Bona–Mahony equation in a finite domain. This particular problem arises from the phenomenon of long wave with small amplitude in fluid. For certain initial-boundary problems for the Korteweg-de Vries–Benjamin–Bona–Mahony equation, we obtain the conditions of blowing-up of global and travelling wave solutions in finite time. The proof of the results is based on the nonlinear capacity method. In closing, we provide the exact and numerical examples.
Keywords: breaking waves, Korteweg-de Vries–Benjamin–Bona–Mahony equation, blow-up of solution, initial-boundary problems.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP05131044
The second named author is financially supported by a grant from the Ministry of Science and Education of the Republic of Kazakhstan (Grant No. AP05131044).
Received: 09.10.2018
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35K55, 35R11
Language: English
Citation: M. Kirane, B. T. Torebek, “On a nonlinear problem of the breaking water waves”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 12:2 (2019), 37–46
Citation in format AMSBIB
\Bibitem{KirTor19}
\by M.~Kirane, B.~T.~Torebek
\paper On a nonlinear problem of the breaking water waves
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2019
\vol 12
\issue 2
\pages 37--46
\mathnet{http://mi.mathnet.ru/vyuru486}
\crossref{https://doi.org/10.14529/mmp190203}
\elib{https://elibrary.ru/item.asp?id=38225235}
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