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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 3, Pages 447–458 (Mi zvmmf10695)  

This article is cited in 1 scientific paper (total in 1 paper)

Solution blow-up in a nonlinear system of equations with positive energy in field theory

M. O. Korpusov

Faculty of Physics, Moscow State University, Moscow, Russia

Abstract: A problem for a nonlinear system of electromagnetic equations in the Coulomb calibration with allowance for sources of free-charge currents is considered. The local-in-time solvability in the weak sense of the corresponding initial-boundary value problem is proved by applying the method of a priori estimates in conjunction with the Galerkin method. A modified Levine method is used to prove that, for an arbitrary positive initial energy, under a certain initial condition on the functional $\Phi(t)=\int\limits_{\Omega}|\mathbf{A}|^2dx$, where $\mathbf{A}(x)$ is a vector potential, the solution of the initial-boundary value problem blows up in finite time. An upper bound for the blow-up time is obtained.

Key words: finite-time blow-up, generalized Klein–Gordon equations, nonlinear hyperbolic equations, nonlinear initial-boundary value problems, field theory.

DOI: https://doi.org/10.7868/S0044466918030110

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:3, 425–436

Bibliographic databases:

UDC: 517.957
Received: 01.12.2016
Revised: 27.04.2017

Citation: M. O. Korpusov, “Solution blow-up in a nonlinear system of equations with positive energy in field theory”, Zh. Vychisl. Mat. Mat. Fiz., 58:3 (2018), 447–458; Comput. Math. Math. Phys., 58:3 (2018), 425–436

Citation in format AMSBIB
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\paper Solution blow-up in a nonlinear system of equations with positive energy in field theory
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2018
\vol 58
\issue 3
\pages 447--458
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\crossref{https://doi.org/10.7868/S0044466918030110}
\elib{https://elibrary.ru/item.asp?id=32615747}
\transl
\jour Comput. Math. Math. Phys.
\yr 2018
\vol 58
\issue 3
\pages 425--436
\crossref{https://doi.org/10.1134/S0965542518030077}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. O. Korpusov, “Blow-up and global solubility in the classical sense of the Cauchy problem for a formally hyperbolic equation with a non-coercive source”, Izv. Math., 84:5 (2020), 930–959  mathnet  crossref  crossref  mathscinet  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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