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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 9, Pages 1503–1512
DOI: https://doi.org/10.31857/S0044466920090100 (Mi zvmmf11129) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Analytical-numerical study of finite-time blow-up of the solution to the initial-boundary value problem for the nonlinear Klein–Gordon equation

M. O. Korpusov, A. N. Levashov, D. V. Lukyanenko

Faculty of Physics, Lomonosov Moscow State University, Moscow, 119992 Russia
Citations (2)
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DOI: https://doi.org/10.31857/S0044466920090100
Abstract: An analytical-numerical approach is used to study the finite-time blow-up of the solution to the initial boundary-value problem for the nonlinear Klein–Gordon equation. An analytical analysis yields an upper estimate for the blow-up time of the solution with an arbitrary positive initial energy. With the use of this a priori information, the blow-up process is numerically analyzed in more detail. It is shown that the numerical analysis of the blow-up of the solution makes it possible to improve the analytical estimate and to detect local blow-up with respect to the spatial variable.
Key words: partial differential equations, numerical analysis of the solution's blow-up.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 5-100
Received: 11.06.2018
Revised: 10.12.2019
Accepted: 09.04.2020
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 9, Pages 1452–1460
DOI: https://doi.org/10.1134/S0965542520090109
Bibliographic databases:
Document Type: Article
UDC: 517.957
Language: Russian
Citation: M. O. Korpusov, A. N. Levashov, D. V. Lukyanenko, “Analytical-numerical study of finite-time blow-up of the solution to the initial-boundary value problem for the nonlinear Klein–Gordon equation”, Zh. Vychisl. Mat. Mat. Fiz., 60:9 (2020), 1503–1512; Comput. Math. Math. Phys., 60:9 (2020), 1452–1460
Citation in format AMSBIB
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\paper Analytical-numerical study of finite-time blow-up of the solution to the initial-boundary value problem for the nonlinear Klein--Gordon equation
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\pages 1503--1512
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