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（PDE）在数学、科学和工程的许多领域都有着广泛的应用.它们的数值解一直是一个重要而热门的研究领域。是次会议将集中讨论非线性椭圆偏微分方程数值解的主要观点及最新成果，并为未来研究指明方向。Glowinski，他将提供十个讲座，介绍一组相对较大的方法，允许各种非线性偏微分方程的数值解。讲座将特别注意基于相对简单的组件的模块化方法。讲座将讨论非线性特征值问题的解决方案，完全非线性椭圆方程的蒙赫-安培型和一些椭圆变分不等式从连续力学。会议将作为一个论坛，研究人员在不同方面的数值解和非线性偏微分方程的应用进行互动，交流和促进新的想法，成果和技术解决非线性椭圆偏微分方程及其跨学科的应用。它还将为研究生和年轻的数学家提供一个机会，快速学习该领域的新问题和技术。这将极大地促进非线性椭圆偏微分方程数值方法的研究，并将有助于扩大国家的人才基础，为下一代的数值分析和计算科学家。

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.