CBMS Regional Conference in the Mathematical Sciences - Numerical Methods for Nonlinear Elliptic Equations - Spring 2007

非线性椭圆型偏微分方程（PDEs）在数学、科学和工程的许多领域都有应用。它们的数值解一直是一个重要而热门的研究领域。会议将汇集非线性椭圆偏微分方程数值解的主要思想和最新成果，并为今后的研究指明方向。首席讲师是国际知名的专家R. Glowinski教授，他将提供十场讲座，介绍一系列相对较大的方法，这些方法允许各种非线性偏微分方程的数值解。讲座将特别关注基于相对简单组件的模块化方法。讲座将讨论非线性本征值问题的解，全非线性蒙日-安培型椭圆方程的解，以及连续介质力学中一些椭圆变分不等式的解。会议将为研究非线性偏微分方程数值解和应用的不同方面的研究人员提供一个论坛，以交流和促进求解非线性椭圆偏微分方程及其跨学科应用的新思想、新结果和新技术。它还将为研究生和年轻数学家提供一个快速学习该领域新问题和技术的机会。这将极大地促进非线性椭圆偏微分方程数值方法的研究，并有助于扩大我国培养下一代数值分析和计算科学家的人才基础。

Nonlinear elliptic partial differential equations (PDEs) arise in many areas of mathematics, sciences and engineering. Their numerical solution has continued to be an important and popular research field. The conference will pull together the major ideas and recent results on numerical solution of nonlinear elliptic PDEs and chart directions for future research.The Principal Lecturer is an internationally well-known expert, Professor R. Glowinski, who will deliver ten lectures on a relatively large set of methods allowing the numerical solution of a variety of nonlinear PDEs. Particular attention of the lectures will be given to modular methods based on relatively simple components. The lectures will discuss the solution of nonlinear eigenvalue problems, of fully nonlinear elliptic equations of the Monge-Ampere type and of some elliptic variational inequalities from Continuum Mechanics. The conference will serve as a forum for researchers working on different aspects of numerical solution and applications of nonlinear PDEs to interact and to exchange and promote new ideas, results and techniques on solving nonlinear elliptic PDEs and their interdisciplinary applications. It will also provide an opportunity for graduate students and young mathematicians to learn quickly new problems and techniques in the area. It will greatly contribute to the advancement of research on numerical methods for nonlinear elliptic PDEs, and will help to enlarge the personnel base of the nation for next generation numerical analysts and computational scientists.