Solution blow-up in a nonlinear system of equations with positive energy in field theoryстатья
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Дата последнего поиска статьи во внешних источниках: 6 декабря 2018 г.
Аннотация: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 Φ(t)=∫ Ω |A| 2 dx
Φ(t)=∫Ω|A|2dx
, where A(x)
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.