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.
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
\Bibitem{KorLevLuk20}
\by M.~O.~Korpusov, A.~N.~Levashov, D.~V.~Lukyanenko
\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.
\yr 2020
\vol 60
\issue 9
\pages 1452--1460
\crossref{https://doi.org/10.1134/S0965542520090109}
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Linking options:
https://www.mathnet.ru/eng/zvmmf11129
https://www.mathnet.ru/eng/zvmmf/v60/i9/p1503
This publication is cited in the following 2 articles:
O. N. Shablovskii, “Primery tochnykh reshenii nelokalnogo volnovogo uravneniya s nelineinymi istochnikami”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 15:4 (2023), 30–37
Cong Sun, Dong Ze Yan, Yong Ling Zhang, “Global existence and blow up of the solution for nonlinear Klein-Gordon equation with variable coefficient nonlinear source term”, Open Mathematics, 20:1 (2022), 931
Citation in format AMSBIB
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