The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
In this talk we study a semilinear system involving the operator curl, which is the limiting form of Ginzburg-Landau model for superconductors in R3 for a large value of the Ginzburg-Landau parameter. We consider the location of the maximum points of the magnitude of solutions, which corresponds to the nucleation of instability of the Meissner state for superconductors when the applied field is increased in the transition between superconducting and mixed states. For small penetration depth, we prove that the location not only depends on the tangential component of the applied magnetic field, but also on the normal curvature of the boundary in some direction. We also show that the solutions decay exponentially away from the boundary if the penetration depth is small.
Xingfei Xiang holds his Ph.D. from ECNU in June 2012. Now he is an assistant professor of mathematics at Tongji University. His current interests are the estimates for vector fields and their applications to PDEs, in particular on the estimate in the L1 space.