Title: The well-posedness of the Korteweg-de Vries equation in a 
       quarter plane or a finite domain

Abstract: The talk will discuss initial- and boundary-value
problems (IBVP) for the Korteweg-de Vries (KdV) equation posed 
in a quarter plane and on a bounded interval with nonhomogeneous 
boundary conditions. These problems arise naturally in certain 
circumstances when the KdV equation is used as a model for 
waves and a numerical scheme is needed. It will be shown that 
the IBVP is locally and globally well-posed in certain Banach 
spaces. Then, these well-posedness results will be applied to obtain 
the exact theory of convergence of the two-point boundary value
problem to the quarter-plane boundary value problem, which
provides a justification for the use of the two-point boundary value
problem in numerical studies of the quarter plane problem. 
(This is a joint work with J. Bona and B. Zhang)