On existence results for elliptic and parabolic systems of partial differential equations in superconductivity, some corrections and improvements

This article develops existence results for non-linear partial differential equations in superconductivity. Specifically for the parabolic model, the method of proof comprises a variational approach for establishing a concerning solution existence at each instant of time, related to a model discretized in time. Moreover, as a novelty, we have modeled the Ginzburg-Landau system in superconductivity as a two phase one, with a wave function for a super-conducting phase and another one for a normal phase.