Geodesic
On a nonlinear problem of the breaking water waves
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 2, pp. 37-46

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{VYURU_2019_12_2_a2,
     author = {M. Kirane and B. T. Torebek},
     title = {On a nonlinear problem of the breaking water waves},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {37--46},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2019_12_2_a2/}
}
TY  - JOUR
AU  - M. Kirane
AU  - B. T. Torebek
TI  - On a nonlinear problem of the breaking water waves
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2019
SP  - 37
EP  - 46
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VYURU_2019_12_2_a2/
LA  - en
ID  - VYURU_2019_12_2_a2
ER  - 
%0 Journal Article
%A M. Kirane
%A B. T. Torebek
%T On a nonlinear problem of the breaking water waves
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2019
%P 37-46
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VYURU_2019_12_2_a2/
%G en
%F VYURU_2019_12_2_a2
M. Kirane; B. T. Torebek. On a nonlinear problem of the breaking water waves. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 2, pp. 37-46. http://geodesic.mathdoc.fr/item/VYURU_2019_12_2_a2/