标题： 超导体在强电流存在下的正常态的全局稳定性 显示英文标题

标题： Global stability of the normal state of superconductors in the presence of a strong electric current

摘要： 我们考虑在存在通过二维导线的电流情况下超导性的时变Ginzburg-Landau模型。 我们证明当电流足够强时，解在长时间极限下收敛到正常状态。 我们提供了两种类型的临界电流上界，其中实现了这种全局稳定性：通过使用与正常磁场相关的磁拉普拉斯算子的主特征值，以及通过线性化稳态算子的预解算子的范数。 在后一种情况下，我们通过定义在平面上和半平面上的近似算子的范数来估计大区域中预解算子的范数。 我们还通过获得使正常状态失去局部稳定性时的电流，得到了大区域中上述临界电流的下界。 显示英文摘要

摘要： We consider the time-dependent Ginzburg-Landau model of superconductivity in the presence of an electric current flowing through a two-dimensional wire. We show that when the current is sufficiently strong the solution converges in the long-time limit to the normal state. We provide two types of upper bounds for the critical current where such global stability is achieved: by using the principal eigenvalue of the magnetic Laplacian associated with the normal magnetic field, and through the norm of the resolvent of the linearized steady-state operator. In the latter case we estimate the resolvent norm in large domains by the norms of approximate operators defined on the plane and the half-plane. We also obtain a lower bound, in large domains, for the above critical current by obtaining the current for which the normal state looses its local stability.