Mathematical Sciences: Floquet Theory for Periodic PDE

这个项目将研究Floquet指数，Floquet 展开，以及椭圆和 周期系数抛物方程 重点将 放在对Floquet集合几何的理解上 指数，Floquet解的展开式， 以及Floquet指数几何之间的联系 以及给定方程的性质。 这些研究的动机是一些领域出现的问题， 数学物理学，如稳定性理论，量子理论， 固体、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.