Geodesic
Blow-up of solutions of a~full non-linear equation of ion-sound waves
Izvestiya. Mathematics , Tome 82 (2018) no. 2, pp. 283-317

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

We consider a series of initial-boundary value problems for the equation of ion-sound waves in a plasma. For each of them we prove the local (in time) solubility and perform an analytical-numerical study of the blow-up of solutions. We use the method of test functions to obtain sufficient conditions for finite-time blow-up and an upper bound for the blow-up time. In concrete numerical examples we improve these bounds numerically using the mesh refinement method. Thus the analytical and numerical parts of the investigation complement each other. The time interval for the numerical modelling is chosen in accordance with the analytically obtained upper bound for the blow-up time. In return, numerical calculations specify the moment and pattern of this blow-up.
Keywords: blow-up of a solution, non-linear initial-boundary value problem, exponential non-linearity, Richardson extrapolation.
Mots-clés : Sobolev-type equations 
@article{IM2_2018_82_2_a2,
     author = {M. O. Korpusov and D. V. Lukyanenko and A. A. Panin and E. V. Yushkov},
     title = {Blow-up of solutions of a~full non-linear equation of ion-sound waves},
     journal = {Izvestiya. Mathematics },
     pages = {283--317},
     publisher = {mathdoc},
     volume = {82},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_2_a2/}
}
TY  - JOUR
AU  - M. O. Korpusov
AU  - D. V. Lukyanenko
AU  - A. A. Panin
AU  - E. V. Yushkov
TI  - Blow-up of solutions of a~full non-linear equation of ion-sound waves
JO  - Izvestiya. Mathematics 
PY  - 2018
SP  - 283
EP  - 317
VL  - 82
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2018_82_2_a2/
LA  - en
ID  - IM2_2018_82_2_a2
ER  - 
%0 Journal Article
%A M. O. Korpusov
%A D. V. Lukyanenko
%A A. A. Panin
%A E. V. Yushkov
%T Blow-up of solutions of a~full non-linear equation of ion-sound waves
%J Izvestiya. Mathematics 
%D 2018
%P 283-317
%V 82
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2018_82_2_a2/
%G en
%F IM2_2018_82_2_a2
M. O. Korpusov; D. V. Lukyanenko; A. A. Panin; E. V. Yushkov. Blow-up of solutions of a~full non-linear equation of ion-sound waves. Izvestiya. Mathematics , Tome 82 (2018) no. 2, pp. 283-317. http://geodesic.mathdoc.fr/item/IM2_2018_82_2_a2/