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

9708261 Chen本奖学金将为西北大学“1997- 1998年非线性偏微分方程及其应用重点年”提供部分资助。这个特殊年度的目标是发展非线性偏微分方程与流体力学、相变、自由边界问题、材料科学和平均曲率流等不同领域之间的一些新联系。这个重点年的重点将是在1998年春季举行的非线性偏微分方程及其应用国际会议。在这一年中，计划对指定领域的专家和初级研究人员进行一系列访问。非线性偏微分方程几乎出现在所有的科学和工程领域。特别是，它们出现在材料科学、生物物理学、环境和全球变化过程以及工业制造过程中。这些方程在弹性、塑性、半导体、离子的生物传输、相变、多相过程、燃烧、蚀刻和沉积过程等领域占主导地位。理解这些非线性方程的解可以使人们获得新的物理见解，发现内在规律，进而解决这些领域的一些具有挑战性的问题。提议的项目旨在汇集不同群体的应用数学家和偏微分方程及其应用的理论分析师，他们能够探索各自领域之间的联系。将选择能够分享专业知识的个人，并着眼于西北大学教师所代表的应用科学和其他数学领域的指定领域的应用。拥有如此多样化专业知识的研究人员往往有尚未开发的共同兴趣，通过富有成效的交流，可以产生新的结果和发现。我们将特别关注近期博士和/或研究生的参与，以培养他们对非线性偏微分方程及其在科学和工程中的应用的兴趣。

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.