L_p-Solvability of a Full Superconductive Modelстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 10 августа 2018 г.
Аннотация:In this article the mean-field vortex model arising from the II-type superconductivity is investigated. The vortex model is reduced to a nonlinear hyperbolic–elliptic system of PDEs in a bounded domain. Motivated by experiments, we consider physical boundary conditions, which describe a flux of superconducting vortices through the boundary of the domain. We prove the global solvability for the system. To show the solvability result we take a vanishing “viscosity” limit in an approximated parabolic–elliptic system. Since the approximated solutions do not have a compactness property, we justify this limit transition, using a kinetic formulation of our problem. The main trick is that instead of the nonlinear system, we have to investigate a linear transport equation.