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Slightly below the transition temperatures, the behavior of superconducting materials is governed by the Ginzburg-Landau (GL) equation which characterizes the dynamical interaction of the density of superconducting electron pairs and the exited electromagnetic potential. In this paper, an optimal control problem of the strength of external magnetic field for one-dimensional thin film superconductors...
Sufficient conditions for the existence of solutions to stochastic inclusions $x_t - x_s ∈ ∫^t_s F_τ(x_τ)dτ + ∫^t_s G_τ(x_τ)dw_τ + ∫^t_s∫_{IRⁿ} H_{τ,z}(x_τ)ν̃ (dτ,dz)$ beloning to a given set K of n-dimensional cádlág processes are given.
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