Mathematical Sciences: Floquet Theory for Periodic PDE

本课题将研究具有周期系数的椭圆型和抛物型方程的Floquet指数、Floquet展开式以及解的相关性质。重点将放在了解弗洛奎指数集的几何、解在弗洛奎解方面的展开、以及弗洛奎指数的几何与给定方程的性质之间的联系。这些研究的动机是数学物理领域中出现的问题，如稳定性理论、固体量子理论、流体动力学和逆散射理论。

This project will investigate Floquet exponents, Floquet expansions, and related properties of solutions to elliptic and parabolic equations with periodic coefficients. Emphasis will be placed on the understanding of the geometry of the set of Floquet exponents, expansion of solutions in terms of Floquet solutions, and the connections between the geometry of the Floquet exponents and the properties of the given equation. These studies have been motivated by problems arising in areas of mathematical physics such as stability theory, quantum theory of solids, hydrodynamics, and inverse scattering theory.