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Izvestiya: Mathematics, 2018, Volume 82, Issue 2, Pages 283–317
DOI: https://doi.org/10.1070/IM8579 (Mi im8579) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Blow-up of solutions of a full non-linear equation of ion-sound waves in a plasma with non-coercive non-linearities

M. O. Korpusova, D. V. Lukyanenkoa, A. A. Paninab, E. V. Yushkovac

a Lomonosov Moscow State University, Faculty of Physics
b Nikol'skii Mathematical Institute of Peoples’ Friendship University of Russia
c Space Research Institute, Russian Academy of Sciences, Moscow
English version PDF (632 kB) Citations (11)
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DOI: https://doi.org/10.1070/IM8579
Abstract: We consider a series of initial-boundary value problems for the equation of ion-sound waves in a plasma. For each of them we prove the local (in time) solubility and perform an analytical-numerical study of the blow-up of solutions. We use the method of test functions to obtain sufficient conditions for finite-time blow-up and an upper bound for the blow-up time. In concrete numerical examples we improve these bounds numerically using the mesh refinement method. Thus the analytical and numerical parts of the investigation complement each other. The time interval for the numerical modelling is chosen in accordance with the analytically obtained upper bound for the blow-up time. In return, numerical calculations specify the moment and pattern of this blow-up.
Keywords: blow-up of a solution, non-linear initial-boundary value problem, Sobolev-type equations, exponential non-linearity, Richardson extrapolation.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-03524
16-32-00011
16-01-00755
16-01-00437
14-01-00182
14-01-00208
This paper was written with the support of the Russian Foundation for Basic Research (grants nos. 15-01-03524, 16-32-00011, 16-01-00755, 16-01-00437, 14-01-00182 and 14-01-00208).
Received: 11.06.2016
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2018, Volume 82, Issue 2, Pages 43–78
DOI: https://doi.org/10.4213/im8579
Bibliographic databases:
Document Type: Article
UDC: 517.957+519.6
MSC: 35B44, 35L35, 35Q60, 76X05
Language: English
Original paper language: Russian
Citation: 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. RAN. Ser. Mat., 82:2 (2018), 43–78; Izv. Math., 82:2 (2018), 283–317
Citation in format AMSBIB
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\paper Blow-up of solutions of a~full non-linear equation of ion-sound waves
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\jour Izv. RAN. Ser. Mat.
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\vol 82
\issue 2
\pages 43--78
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:85
    English version PDF:19
    References:55
    First page:34
     
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