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 \(\Phi (t) = \int\limits_\Omega {|A{|^2}dx} \), 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.
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Original Russian Text © M.O. Korpusov, 2018, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2018, Vol. 58, No. 3, pp. 447–458.
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Korpusov, M.O. Solution Blow-up in a Nonlinear System of Equations with Positive Energy in Field Theory. Comput. Math. and Math. Phys. 58, 425–436 (2018). https://doi.org/10.1134/S0965542518030077
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DOI: https://doi.org/10.1134/S0965542518030077