Mathematical Sciences: Linear and Non-Linear Waves

本项目将研究碰撞等离子体的稳定性和平衡，标量波方程束缚态的不稳定性和散射特性，时间周期系统的散射频率，线性和非线性色散波的规律性。基本数学问题集中于某些初值问题的整体存在性。这些对线性和非线性波的研究在天体物理学和热核融合等领域得到了应用。

This project will investigate stability and equilibria in plasma with collisions, instabilities and scattering properties of bound states of scalar wave equations, scattering frequencies of time periodic systems, and regularity of linear and nonlinear dispersive waves. The fundamental mathematical problems focus on global existence for certain initial value problems. These studies in linear and nonlinear waves find applications in fields such as astrophysics and thermonuclear fusion.