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.

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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 
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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/

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