U.S.-China Cooperative Research (Mathematics): Function Theoretic Methods in Partial Differential Equations

这是特拉华大学的罗伯特·P·吉尔伯特与来自北京大学、上海复旦大学和广州中山大学的四位中国数学家进行的为期两年的合作研究项目。该项目由美国国家自然科学基金会和中国国家自然科学基金资助。偏微分方程是描述物理科学和工程中许多问题的方法。这些应用领域的进展在很大程度上取决于偏微分方程求解方法的发展和这些方法的数值实施。目前这种相互关系最明显的两个领域是注塑成型和复合材料壳体的设计。注射成型过程可以用Hele.Shaw流来描述，而Hele.Shaw流又是数学家所说的“椭圆移动边界问题”。组合弹性壳由椭圆型方程组描述。这个合作项目的目标是通过使用“函数论”方法及其数值实现来更好地理解这些问题。在这一领域特别强大的中国合作科学家是：北京大学的温国春，复旦的徐振元和侯宗毅，以及中山的林伟。这些科学家中的每一位都将在特拉华大学与吉尔伯特教授和他的研究小组合作几个月。

This is a two.year collaborative research project between Robert P. Gilbert of the University of Delaware and four Chinese mathematicians from Beijing University, Fudan University in Shanghai, and Zhongshan University in Guangzhou. The project is sponsored by NSF and the Chinese National Natural Science Foundation. Partial differential equations are the means by which many problems in the physical sciences and engineering are described. Progress in these applied fields is dependent to a large degree on progress in the development of methods for solving partial differential equations and the numerical implementation of these methods. Two current areas where this interrelation is most apparent is in the area of injection molding and the design of composite shells. The injective molding procedure may be described by a Hele.Shaw flow, which in turn is what mathematicians refer to as an "elliptic moving boundary problem." The composite elastic shells are described by an elliptic system of equations. The goal of this collaborative project is to reach a better understanding of these problems, using "function theoretic" methods and their numerical implementation. The Chinese collaborating scientists, who are especially strong in this field are: Wen Guochun from Beijing University, Xu Zhenyuan and Hou Zongyi from Fudan, and Lin Wei from Zhongshan. Each of these scientists will spend a few months working with Professor Gilbert and his research group at the University of Delaware.