Behavior of Solutions to Time-Dependant and Inhomogenous Ginzburg-Landau Models

时间依赖和非齐次金兹堡-朗道模型解的行为拟建研究摘要peter J . Sternberg这个项目是对一些已被提议作为超导体模型的方程进行严格的研究。特别地，我们将研究具有外加电流的时变金兹堡-朗道方程的某些解，并研究某些稳态的稳定性，“非拓扑”涡旋的可能形成以及正流和超流的共存。超导是一个重要的课题，但其数学建模还不发达。根据这一建议，我们将与一些同事和学生合作，进一步发展一些公认方程的数学分析，并解释观察到的现象。

Behavior of Solutions to Time-dependent and InhomogeneousGinzburg-Landau ModelsAbstract of Proposed ResearchPeter J Sternberg This project is to conduct a rigorous investigation of some equations that have been proposed as models for superconductors. In particular, we shall study certain solutions of the time-dependent Ginzburg-Landau equations with applied currents and investigate the stability of certain steady states, the possible formation of "non-topological" vortices and the co-existence of normal and supercurrents. Superconductivity is an important topic whose mathematical modeling is poorly developed. Under this proposal, and in collaboration with some colleagues and students, we aim to further develop the mathematical analysis of some of the accepted equations and explain the observed phenomena.