On the Ginzburg-Landau model in the presence of an externally imposed magnetic field

1.结果表明，对外加磁场下超导体中镶嵌态的唯象描述方法，导致考虑在磁场从超导体各部分完全排出的约束下吉布斯自由能的最小化问题.考虑含时Ginzburg-Landau-麦克斯韦方程组的初边值问题.利用Fadeo-Galerkin方法建立了L_2弱解或强解的整体存在唯一性定理。对于抛物型方程，利用半群方法得到了L_3解的局部存在性.用有限差分法对抛物型含时Ginzburg-Landan-麦克斯韦方程组的解进行了数值实验。

1. It is shown that a way of phenomenological description of the mosaic state in a superconductor under an applied magnetic field leads to consider the minimizing problem of the Gibbs free energy under the constraints of complete expulsion of magnetic field from the parts of superconductor.2. The initial-boundary value problem for the time-dependent Ginzburg-Landau-Maxwell equations is considered. The global existence and uniqueness theorems of L_2 weak or strong solutions are established via Fadeo-Galerkin's method. As to the parabolic version, the local existence of L_3 solutions is obtained by the semigroup approach for both bounded and exterior problems.3. Numerical experiments of solutions to the parabolic version of the time dependent Ginzburg-Landan-Maxwell equations are obtained by the finite difference methods.