The Existence And Uniqueness Of One Dimension Superconductivity Equations And Numerical Approximations

In this paper, we study the existence and uniqueness of superconductivity equations under Neumann boundary conditions. We also describe some numerical approximations of solutions to the model equations. Most problems of the superconductor physics can be concluded as solving a corresponding boundary condition Integral-Differential equation. The main purpose of this paper is to discuss a new model of superconducting materials developed in [2] and [14]. The rest of this paper is laid out as follows. First based on the physics principles, the London Theory and the Pippard's Theory, derived the solving equation of the problem, that is the Ginzburg-Landau equation of the superconducting materials. Then by using some integral identical equations we present the existence and uniqueness of Neumann boundary conditions of superconductivity equations. One of the keys of this process is to use the integral identical equations. Based on the Euler-Maclaurin expansion, we present the Nystrom method and asymptotic expansion of the first kind weak-singularity integral-differential equations of...