Speaker: Dionyssis Mantzavinos, University of Kansas
Date: February 17, 2022
Title: Initial-boundary value problems for nonlinear dispersive PDEs in one and two dimensions
Abstract: It is often the case in physical and other applications that nonlinear dispersive PDEs arise in domains with a boundary. Such situations lead to the formulation of initial-boundary value problems, which are generally supplemented with various types of nonzero boundary conditions. In this talk, we will discuss a general method for establishing the well-posedness (i.e. existence & uniqueness of solution, and its continuous dependence on the data) of such initial-boundary value problems. Our main vehicle for doing so will be the nonlinear Schrödinger equation. Importantly, we will focus on recent progress on the analysis of this equation in two spatial dimensions. This talk is based on joint works with Thanasis Fokas, Alex Himonas and Fangchi Yan.