Emphasis Year: Nonlinear Partial Differential Equations and Their Applications; Spring, 1998; Evanston, Illinois

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9708261 Chen This award will provide partial support for the 1997-98 Emphasis Year in Nonlinear Partial Differential Equations and Their Applications at Northwestern University. The goal of this special year is to develop some of the new connections between nonlinear partial differential equations and such diverse areas as fluid mechanics, phase transitions, free boundary problems, materials science, and mean curvature flow. The focus of this emphasis year will be an International Conference on Nonlinear Partial Differential Equations and Applications in the Spring of 1998. During the year, a series of visits of experts and junior researchers in the indicated areas is planned. Nonlinear partial differential equations arise in almost all areas of science and engineering. In particular, they arise in materials science, biophysics, environmental and global change processes, and industrial manufacturing processes. These equations are predominant in such areas as elasticity, plasticity, semiconductors, biological transport of ions, phase transitions, multi-phase processes, combustion, and etching and deposition processes. Understanding solutions of such nonlinear equations enables one to gain new physical insights, to discover the intrinsic laws, and, in turn, to solve some challenging problems in these areas. The proposed project is intended to bring together a diverse group of applied mathematicians and theoretical analysts in partial differential equations and their applications who are able to explore connections between their fields. Individuals will be selected who can share expertise with an eye toward applications in the indicated areas in applied sciences and other mathematical areas represented by the Northwestern faculty. Researchers with such diverse expertise have often unexplored common interests which, by means of fruitful exchanges, can lead to novel results and discoveries. Particular attention will be focused on the p articipation of recent doctoral recipients and/or graduate students in order to foster their interests in nonlinear partial differential equations and applications in science and engineering.