Mathematical Sciences: Floquet Theory for Periodic PDE

本项目将研究周期系数椭圆型和抛物型方程解的Floquet指数、Floquet展开和相关性质。重点将放在理解Floquet指数集合的几何形状，用Floquet解展开解，以及Floquet指数几何形状与给定方程性质之间的联系。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.