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

美国-意大利奖将支持约翰霍普金斯大学的Clifford Truesdell教授、Reza Malek-Madani教授、John Pierce教授在比萨大学的Gianfranco Capriz教授的领导下与意大利数学家进行合作。研究人员打算对最近由特鲁斯戴尔教授开始的连续介质力学数学基础的重组进行研究。在此过程中，他们期望解决拓扑、功能分析和几何测量理论中的相关问题。要研究的课题包括：一类Navier-Stokes方程的解，控制非线性粘性材料变形的拟线性椭圆型和抛物型微分方程系统奇点的形成和稳定性，对非线性弹性中出现的高度对称边值问题的平衡的研究，以及奇点数学理论的各个方面，这些方面有助于连续介质力学和应用数学。双方的研究人员在连续介质力学的各个方面都是领先的专家，他们的合作有望在该领域带来新的方法。本研究由美国国家科学基金会固体力学和美国-意大利项目联合资助。

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.