Solution Blow-up in a Nonlinear System of Equations with Positive Energy in Field Theory
- Autores: Korpusov M.O.1
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Afiliações:
- Faculty of Physics
- Edição: Volume 58, Nº 3 (2018)
- Páginas: 425-436
- Seção: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/180111
- DOI: https://doi.org/10.1134/S0965542518030077
- ID: 180111
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Resumo
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 \(\Phi (t) = \int\limits_\Omega {|A{|^2}dx} \), where 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.
Sobre autores
M. Korpusov
Faculty of Physics
Autor responsável pela correspondência
Email: korpusov@gmail.com
Rússia, Moscow, 119991
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