Solution Blow-up in a Nonlinear System of Equations with Positive Energy in Field Theory


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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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M. Korpusov

Faculty of Physics

编辑信件的主要联系方式.
Email: korpusov@gmail.com
俄罗斯联邦, Moscow, 119991

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