Geodesic
Local Solvability and Global Unsolvability of a Model of Ion-Sound Waves in a Plasma
Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 426-441

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

An initial-boundary value problem for the multidimensional equation of ion-sound waves in a plasma is considered. Its time-local solvability in the classical sense in Hölder spaces is proved. This is a development of results in our previous papers, where the local solvability of one-dimensional analogs of the equation under consideration was established and, in the general case (regardless of the dimension of the space), sufficient conditions for the blow-up of the solution were obtained.
Keywords: nonlinear initial-boundary value problem, exponential nonlinearity.
Mots-clés : Sobolev-type equations 
@article{MZM_2020_107_3_a8,
     author = {A. A. Panin and G. I. Shlyapugin},
     title = {Local {Solvability} and {Global} {Unsolvability} of a {Model} of {Ion-Sound} {Waves} in a {Plasma}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {426--441},
     publisher = {mathdoc},
     volume = {107},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a8/}
}
TY  - JOUR
AU  - A. A. Panin
AU  - G. I. Shlyapugin
TI  - Local Solvability and Global Unsolvability of a Model of Ion-Sound Waves in a Plasma
JO  - Matematičeskie zametki
PY  - 2020
SP  - 426
EP  - 441
VL  - 107
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a8/
LA  - ru
ID  - MZM_2020_107_3_a8
ER  - 
%0 Journal Article
%A A. A. Panin
%A G. I. Shlyapugin
%T Local Solvability and Global Unsolvability of a Model of Ion-Sound Waves in a Plasma
%J Matematičeskie zametki
%D 2020
%P 426-441
%V 107
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a8/
%G ru
%F MZM_2020_107_3_a8
A. A. Panin; G. I. Shlyapugin. Local Solvability and Global Unsolvability of a Model of Ion-Sound Waves in a Plasma. Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 426-441. http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a8/