U.S.-Italy Cooperative Research: The Foundations of Continuum Mechanics and Untypical Problems

这个美国-意大利奖将支持教授克利福德 Truesdell，Reza Malek-Madani和约翰的约翰皮尔斯 霍普金斯大学与意大利数学家合作 在Gianfranco Capriz教授的领导下， 比萨大学。 调查人员打算在 最近重组的数学基础， 由特鲁斯戴尔教授开创的连续介质力学 在 在这个过程中，他们希望解决拓扑学中的相关问题， 功能分析和几何测量理论。 其中要研究的主题是类的解决方案， Navier-Stokes方程的形成和稳定性 拟线性椭圆型和抛物型方程组的奇性 微分方程控制的变形 非线性粘性材料的平衡研究 高度对称的边值问题， 非线性弹性，以及数学的各个方面， 奇点理论，使其成为连续统 力学和应用数学。 双方的研究人员 是连续介质力学各方面的顶尖专家 他们的合作有望带来新的方法 在外地 这项工作得到了Solid 机械师和美国- NSF的意大利项目。

This U.S.-Italy award will support Professors Clifford Truesdell, Reza Malek-Madani, and John Pierce of Johns Hopkins University to collaborate with Italian mathematicians under the leadership of Prof. Gianfranco Capriz of the University of Pisa. The investigators intend to work on the recent reorganization of the mathematical foundations of continuum mechanics begun by Professor Truesdell. In the process, they expect to solve associated problems in topology, functional analysis, and geometric measure theory. Among the topics to be studied are classes of solutions of Navier-Stokes equations, the formation and stability of singularities in systems of quasilinear elliptic and parabolic differential equations that govern the deformation of nonlinear viscous materials, the study of equilibria for highly symmetric boundary value problems which arise in nonlinear elasticity, and various aspects of the mathematical theory of singularities that lend themselves to continuum mechanics and applied mathematics. Researchers on both sides are leading experts on various aspects of continuum mechanics and their collaboration is expected to lead to new approaches in the field. This work is jointly supported by the Solid Mechanics and U.S.-Italy Programs of NSF.