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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 9, Pages 1503–1512 (Mi zvmmf11129)  

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

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


DOI: https://doi.org/10.31857/S0044466920090100


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:9, 1452–1460

Bibliographic databases:

UDC: 517.957
Received: 11.06.2018
Revised: 10.12.2019
Accepted:09.04.2020

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
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 9
\pages 1503--1512
\mathnet{http://mi.mathnet.ru/zvmmf11129}
\crossref{https://doi.org/10.31857/S0044466920090100}
\elib{https://elibrary.ru/item.asp?id=43832509 }
\transl
\jour Comput. Math. Math. Phys.
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\issue 9
\pages 1452--1460
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