7 papers · 1 filter
Regularity of a Parabolic System Involving Curl
Xing-Bin Pan
This note presents a regularity result with proof for an initial-boundary value problem of a linear parabolic system involving curl of the unknown vector field, subjected to the bo…
Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential (Derivation of the Aharanov-Bohm potential in the Ginzburg-Landau model)
Ayman Kachmar, XingBin Pan
We consider the Aharonov-Bohm magnetic potential and study the transition from normal to superconducting solutions within the Ginzburg-Landau model of superconductivity. We obtain…
General Magneto-Static Model
Xing-Bin Pan
In this paper we study a nonlinear magneto-static model on a general domain which is multiply-connected and has holes, and under a nonlinear relation between magnetic induction…
Existence and Regularity of Weak Solutions for a Thermoelectric Model
Xing-Bin Pan, Zhibing Zhang
This paper concerns a time-independent thermoelectric model with two different boundary conditions. The model is a nonlinear coupled system of the Maxwell equations and an elliptic…
Meissner States of Type II Superconductors
Xing-Bin Pan
This paper concerns mathematical theory of Meissner states of a bulk superconductor of type , which occupies a bounded domain in and is subjected to an applied…
Concentration Behavior and Lattice Structure of Surface Superconductivity
Søren Fournais, Jean-Philippe Miqueu, Xing-Bin Pan
We study the three-dimensional Ginzburg-Landau model of superconductivity for strong applied magnetic fields varying between the second and third critical fields. In this regime, i…