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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 9, Pages 1553–1563 (Mi zvmmf10778)  

This article is cited in 2 scientific papers (total in 2 papers)

Analytic-numerical investigation of combustion in a nonlinear medium

M. O. Korpusov, D. V. Lukyanenko, A. D. Nekrasov

Faculty of Physics, Moscow State University, Moscow, Russia

Abstract: Sufficient conditions of the onset of the blow-up mode for the parabolic equation with double nonlinearity that describes the combustion process in a nonlinear medium are analyzed. A sufficient condition for the initial function under which the time of the solution blow-up of the corresponding initial-boundary value problem for this equation is finite is obtained. An analytical upper bound on the solution existence time is derived. This a priori bound on the solution blow-up time is used for the numerical refinement of the blow-up process. It is shown that the numerical diagnostics of the solution blow-up makes it possible to obtained a better estimate of the solution blow-up time and detect the fact of local blow-up with respect to the spatial variable.

Key words: combustion process, parabolic equation with double nonlinearity, analytical-numerical method.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00186


DOI: https://doi.org/10.31857/S004446690002533-7

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:9, 1499–1509

Bibliographic databases:

UDC: 519.633
Received: 10.10.2017

Citation: M. O. Korpusov, D. V. Lukyanenko, A. D. Nekrasov, “Analytic-numerical investigation of combustion in a nonlinear medium”, Zh. Vychisl. Mat. Mat. Fiz., 58:9 (2018), 1553–1563; Comput. Math. Math. Phys., 58:9 (2018), 1499–1509

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. O. Korpusov, A. K. Matveeva, D. V. Lukyanenko, “Diagnostika mgnovennogo razrusheniya resheniya v nelineinom uravnenii teorii voln v poluprovodnikakh”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:4 (2019), 104–113  mathnet  crossref
    2. A. A. Panin, G. I. Shlyapugin, “Local Solvability and Global Unsolvability of a Model of Ion-Sound Waves in a Plasma”, Math. Notes, 107:3 (2020), 464–477  mathnet  crossref  crossref  mathscinet  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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