Mathematical Sciences: Shock Waves and Conservation Laws

主要研究人员将在非线性守恒律和激波领域进行研究，继续研究共振非线性系统中的基本波和Riemann问题，以及利用这种构造的数值方法的收敛性质。激波是在许多“流”情况下观察到的。陡峭梯度的存在给求解的理论和数值方法带来了严重的困难。鉴于这种现象在现实世界中的广泛存在，对非线性波的定性和定量分析具有重要的科学意义。

The principal investigator will conduct research in the area of nonlinear conservation laws and shock waves, continuing the study of elementary waves and the Riemann problem in resonant nonlinear systems as well as the convergence properties of numerical methods utilizing this construction. Shock waves are the observed in many "flow" situations. The presence of steep gradients leads to serious difficulties in both theoretical and numerical methods for obtaining solutions. The qualitative and quatitative analysis of nonlinear waves is of significant scientific interest in view of the wide spread occurrence of such phenomena in real world situations.