BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Dirichlet-to-Neumann map for evolution PDEs on the half-line with time-periodic boundary conditions - Maria Christina van der Weele (Univers iteit Twente) DTSTART:20230726T080000Z DTEND:20230726T090000Z UID:TALK202792@talks.cam.ac.uk DESCRIPTION:For a well-posed boundary value problem\, a certain number of boundary values must be prescribed as boundary conditions\, while the rest of the boundary values are unknown. The task of determining the unknown b oundary values in terms of the prescribed ones is called the computation o f the &ldquo\;generalised Dirichlet-to-Neumann map&rdquo\;. Here we elabor ate on a new approach for finding the Dirichlet-to-Neumann map in the larg e time limit for evolution PDEs on the half-line\, for the physically sign ificant case of time-periodic boundary conditions [1].The method is illust rated both for linear PDEs (including the heat equation\, the convection-d iffusion equation and the linearised KdV equation) and for integrable nonl inear PDEs\, in particular for the focusing NLS equation. It is shown that the time-dependent part of the Lax pair is instrumental in yielding\, via an elegant algebraic calculation\, the large t asymptotics of the periodi c unknown boundary values in terms of the prescribed periodic boundary dat a. This method is based on earlier work by Lenells and Fokas [2]\, in whic h the NLS equation was treated via a more complicated approach.This is joi nt work with Prof. A. S. Fokas.[1] \; \; A. S. Fokas and M. C. van der Weele. The Unified Transform for Evolution Equations on the Half-Line with Time-Periodic Boundary Conditions. Stud. Appl. Math.\, 147(4):1339-1 368\, 2021.[2] \; \; J. Lenells and A. S. Fokas. The Nonlinear Sch rö\;dinger Equation with t-Periodic Data: II. Perturbative Results. Pr oc. R. Soc. A\, 471:20140926\, 2015. LOCATION:Seminar Room 1\, Newton Institute END:VEVENT END:VCALENDAR