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

Ginzburg-Landau模型的解的行为与时间相关的和不稳定的Ginzburg-Landau模型的解的行为研究建议摘要Peter J斯滕贝格这个项目是对一些已经被提议作为超导体模型的方程进行严格的研究。特别是，我们将研究与时间相关的金-朗道方程与应用电流的某些解决方案，并调查某些稳定状态的稳定性，可能形成的“非拓扑”涡流和正常和超导共存。超导是一个重要的课题，但其数学模型还很薄弱。根据这一建议，并与一些同事和学生合作，我们的目标是进一步发展一些公认的方程的数学分析，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.