Existence and uniqueness for a non-isothermal dynamical Ginzburg–Landau model of superconductivity

In this paper, we present a time-dependent Ginzburg–Landau model which describes the phenomenon of superconductivity taking into account thermal effects. We modify the classical time-dependent Ginzburg–Landau equations by including temperature dependence. We prove that this model is compatible with the laws of thermodynamics. Moreover it allows us to express the critical magnetic field, which distinguishes the superconductive phase from the normal state, as a function of the absolute temperature. The theoretical temperature dependence of the threshold magnetic field agrees with the experimental results. Finally, we prove the existence and the uniqueness of the solutions of the non-isothemal Ginzburg–Landau equations.