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关于边值问题及其渐近性的新视角的区域会议将于2005年5月16-20日在德克萨斯大学泛美分校数学系举行。剑桥大学非线性数学科学系主任阿萨纳西奥斯·福卡斯教授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这一主题发表十次演讲。拟举办的讲座的目的是对分析边值问题及其渐近性的一种新的Fokas方法和Deift-周方法作一个完整而全面的阐述。这些方法是对以下三个问题的统一和重要的推广：(I)解线性偏微分方程组(PDE)及其几种变体的经典变换方法，如映像法和Wiener-Hopf技术；(Ii)线性偏微分方程组的解的Ehrenpreis基本原理的积分表示；(Iii)求解非线性发展方程初值问题的逆散射方法。我们将特别注意可积的非线性发展偏微分方程边值问题的长时间渐近性和零扩散极限。

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.