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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 187, Number 3, Pages 447–454
DOI: https://doi.org/10.4213/tmf8954 (Mi tmf8954) 		 
This article is cited in 4 scientific papers (total in 4 papers)

The finite-time blowup of the solution of an initial boundary-value problem for the nonlinear equation of ion sound waves

M. O. Korpusov

Physics Faculty, Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (384 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf8954
Abstract: We obtain blowup conditions for the solutions of initial boundary-value problems for the nonlinear equation of ion sound waves in a hydrogen plasma in the approximation of “hot” electrons and “heavy” ions. A specific characteristic of this nonlinear equation is the noncoercive nonlinearity of the form ∂t|∇u|2, which complicates its study by any energy method. We solve this problem by the Mitidieri–Pohozaev method of nonlinear capacity.
Keywords: nonlinear capacity, blowup.
Received: 23.04.2015
Revised: 26.10.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 187, Issue 3, Pages 835–841
DOI: https://doi.org/10.1134/S0040577916060040
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. O. Korpusov, “The finite-time blowup of the solution of an initial boundary-value problem for the nonlinear equation of ion sound waves”, TMF, 187:3 (2016), 447–454; Theoret. and Math. Phys., 187:3 (2016), 835–841
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf8954
  • https://doi.org/10.4213/tmf8954
  • https://www.mathnet.ru/eng/tmf/v187/i3/p447
    • This publication is cited in the following 4 articles:
    1. M. O. Korpusov, “Nonlinear equations of the theory of ion-sound plasma waves”, Comput. Math. Math. Phys., 61:11 (2021), 1886–1894  mathnet  mathnet  crossref  crossref  isi  scopus
    2. I. I. Kolotov, A. A. Panin, “On Nonextendable Solutions and Blow-Ups of Solutions of Pseudoparabolic Equations with Coercive and Constant-Sign Nonlinearities: Analytical and Numerical Study”, Math. Notes, 105:5 (2019), 694–706  mathnet  crossref  crossref  mathscinet  isi  elib
    3. 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 in a plasma with non-coercive non-linearities”, Izv. Math., 82:2 (2018), 283–317  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. M. O. Korpusov, D. V. Lukyanenko, E. A. Ovsyannikov, A. A. Panin, “Lokalnaya razreshimost i razrushenie resheniya odnogo uravneniya s kvadratichnoi nekoertsitivnoi nelineinostyu”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:2 (2017), 107–123  mathnet  crossref  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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