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Matematicheskie Zametki, 2020, Volume 107, Issue 3, Pages 426–441
DOI: https://doi.org/10.4213/mzm12324 (Mi mzm12324) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Local Solvability and Global Unsolvability of a Model of Ion-Sound Waves in a Plasma

A. A. Panina, G. I. Shlyapugin

a Lomonosov Moscow State University
Full-text PDF (545 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm12324
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.
Keywords: nonlinear initial-boundary value problem, Sobolev-type equations, exponential nonlinearity.
Funding agency Grant number
Russian Science Foundation 18-11-00042
The work of the first author was supported by the Russian Science Foundation (grant 18-11-00042).
Received: 27.01.2019
English version:
Mathematical Notes, 2020, Volume 107, Issue 3, Pages 464–477
DOI: https://doi.org/10.1134/S0001434620030104
Bibliographic databases:
Document Type: Article
UDC: 517.957
Language: Russian
Citation: A. A. Panin, G. I. Shlyapugin, “Local Solvability and Global Unsolvability of a Model of Ion-Sound Waves in a Plasma”, Mat. Zametki, 107:3 (2020), 426–441; Math. Notes, 107:3 (2020), 464–477
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm12324
  • https://www.mathnet.ru/eng/mzm/v107/i3/p426
    • This publication is cited in the following 1 articles:
    1. M. O. Korpusov, A. A. Panin, “On the blow-up of the solution and on the local and global solvability of the Cauchy problem for a nonlinear equation in Holder spaces”, J. Math. Anal. Appl., 504:2 (2021), 125469  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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