Abstract
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.
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Acknowledgments
The authors wish to express gratitude to their colleagues at the Department of Mathematics of the Physics Faculty of Moscow State University, in particular, Professor M. O. Korpusov, for fruitful cooperation.
Funding
The work of the first author was supported by the Russian Science Foundation (grant 18-11-00042).
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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 3, pp. 426–441.
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Panin, A.A., Shlyapugin, G.I. Local Solvability and Global Unsolvability of a Model of Ion-Sound Waves in a Plasma. Math Notes 107, 464–477 (2020). https://doi.org/10.1134/S0001434620030104
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DOI: https://doi.org/10.1134/S0001434620030104