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.
