NSF/CBMS Regional Conference in the Mathematical Sciences - New Perspectives for Boundary Value Problems and Their Asymptotics; May 16-20, 2005; Edinburg, TX

NSF/CBMS 数学科学区域会议 - 边值问题及其渐近问题的新视角；

• 批准号: 0433445
• 负责人: Lokenath Debnath
• 金额: $ 3.2万
• 依托单位: The University of Texas Rio Grande Valley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-01-01 至 2005-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0433445&HistoricalAwards=false
• 关键词: NSF; CBMS; Regional; Conference; Mathematical

An NSF-CBMS Regional Conference on New Perspectives for Boundary Value Problems and Their Asymptotics is proposed to be held at the Department of Mathematics, University of Texas-Pan American (UTPA), May 16-20, 2005. Professor Athanassios Fokas, Chair of Nonlinear Mathematical Sciences at the University of Cambridge, has agreed to serve as the Principal Lecturer of the conference. Professor Fokas will deliver ten lectures on the topic at the proposed conference. The objective of the proposed lectures is to give a self-contained and comprehensive exposition on a new method of Fokas and on the Deift-Zhou method for the analysis of boundary value problems and their asymptotics. These methods provide a unification as well as significant extension of the following three topics:(i) The classical transform methods for solving linear partial differential equations (PDEs) and several of its variants such as the method of images and the Wiener-Hopf technique,(ii) The integral representation of the solution of linear PDEs in terms of the Ehrenpreis fundamentalprinciple, and(iii) The inverse scattering method for solving the initial value problem for nonlinear evolutionequations. Special attention will be given to both the long time asymptotics and the zerodiffusion limit of boundary value problems for integrable nonlinear evolution PDEs.

建议于 2005 年 5 月 16 日至 20 日在德克萨斯大学泛美分校 (UTPA) 数学系召开 NSF-CBMS 关于边值问题及其渐进性新观点的区域会议。Athanassios Fokas 教授，主席剑桥大学非线性数学科学学院已同意担任本次会议的首席讲师。福卡斯教授将在拟议的会议上就该主题发表十场讲座。 本次讲座的目的是对用于分析边值问题及其渐近问题的 Fokas 新方法和 Deift-Zhou 方法进行独立且全面的阐述。这些方法提供了以下三个主题的统一和显着扩展：（i）求解线性偏微分方程（PDE）的经典变换方法及其几种变体，例如图像方法和 Wiener-Hopf 技术， (ii) 根据 Ehrenpreis 基本原理的线性偏微分方程解的积分表示，以及 (iii) 求解非线性演化方程初值问题的逆散射方法。将特别关注可积非线性演化偏微分方程的边值问题的长时间渐近和零扩散极限。