Mathematical Sciences: Convergence of Approximate Solutions to Conservation Laws

双曲系统的不连续解的数学理论在连续体物理问题的推动下得到了强烈的发展，例如，反应流、多相流和弹塑性流的模型。首席研究员将重点研究这些问题的近似方法及其收敛到物理不连续解。对连续介质物理学中出现的一些基本双曲问题的数值逼近方法的更好理解具有深刻的现实意义。这些想法延续到诸如材料加工等活动中。

The mathematical theory of discontinuous solutions to hyperbolic systems is developing intensively motivated by problems from continuum physics which model reactive flows, multiphase flows, and elastoplastic flows, for example. The principal investigator will focus on methods of approximation for these problems and their convergence to physical discontinuous solutions. A better understanding of the methods of numerical approximation for some fundamental hyperbolic problems arising in continuum physics has profound real world implications. These ideas carry over to such initiatives as materials processing.