US-France Cooperative Research: Conservation Laws in Continuum Mechanics

该奖项将支持马歇尔博士与 斯莱姆罗德、威斯康星州大学和两名法国应用数学- marticians：教授米歇尔Rascle，尼斯大学和 里昂高等师范学校丹尼斯·塞尔教授。 的 该项目的目标是研究解决办法的存在， 在连续介质力学中产生的守恒定律体系。 在 特别是，研究人员将研究衰变，传播 以及使用补偿的工具产生振荡 紧性和Young测度 偏微分的一个重要分支 方程是守恒定律的领域。 事实上，大多数机械 系统由这样的方程描述，例如弹性运动 物体、气体、流体、等离子体等，因此他们的研究 分析和数字是非常重要的。 在 在拟议项目中，调查人员将重点关注以下方面： 1)与一个序列相关联的Young测度的动力学 近似解2）描述守恒律的系统 相变 斯莱姆罗德博士和他的法国同事们 一小群数学家中的主要研究人员， 自然保护中的物理合理性问题分析 法律为 提出的问题的解决将是一个重大的 一个核心问题的理解， 现代应用数学：不连续的动力学， 振荡的、测度值的物理系统。

This award will support collaborative research between Dr. Marshall Slemrod, University of Wisconsin and two French applied mathe- maticians: Professor Michel Rascle, University of Nice and Professor Denis Serre, Ecole Normale Superieure de Lyon. The objective of the project is to study the existance of solutions to systems of conservation laws arising in continuum mechanics. In particular, the investigators will study the decay, propagation and creation of oscillations using the tools of compensated compactness and the Young measure. One of the most important branches of partial differential equations is the area of conservation laws. In fact most mechanical systems are described by such equations, e.g. motion of elastic bodies, gases fluids, plasmas, etc. Hence their study both analytically and numerically is exceptionally important. In the proposed project, the investigators will focus on the following: 1) dynamics of the Young measure associated with a sequence of approximate solutions 2) systems of conservation laws describing phase transitions. Dr. Slemrod and his French colleagues are leading researchers in a small group of mathematicians working on the analysis of physically reasonable problems in conservation laws. Solution of the proposed problems would be a significant step toward the understanding of one of the central problems of modern applied mathematics: the dynamics of discontinuous, oscillatory, measure-valued physical systems.