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 fundamental principle, and (iii) The inverse scattering method for solving the initial value problem for nonlinear evolution equations. Special attention will be given to both the long time asymptotics and the zero diffusion limit of boundary value problems for integrable nonlinear evolution PDEs.
