Mathematical Sciences: Linear and Nonlinear Wave Motion

[902387]劳赫首席研究员将研究双曲型偏微分方程解的定性行为。这些方程控制着能携带尖锐信号的波的传播。研究非线性方程的尖峰前和高频波列解。另一个主要的研究领域是对某一地区波浪的控制、观察或稳定的研究。对双曲型偏微分方程解的性质的理解在许多应用领域都是重要的。

8902387 Rauch The principal investigator will study the qualitative behavior of solutions of hyperbolic partial differential equations. These are the equations which govern the propagation of waves which can carry sharp signals. Studies will be made of sharply peaked fronts and high frequency wave train solutions for nonlinear equations. Another main area of research is the study of the control, observation, or stabilization of waves in a region. The understanding of the behavior of solutions of hyperbolic partial differential equations is important in many fields of application.