Graduate Student / Postdoc Seminar
Corner Singularities, Gibbs Phenomenon and the Unified Transform Method
Speaker: Tom Trogdon
Location: Warren Weaver Hall 1302
Date: Friday, November 13, 2015, 1 p.m.
Abstract: Consider solving a linear, constant-coefficient evolution PDE in one spatial dimension where the initial data vanishes on the negative half line (x < 0). One can interpret this solution, restricted to x > 0, t > 0, as the solution of an initial-boundary value problem where the boundary data is not compatible with the initial data. This solution exhibits a corner singularity. Furthermore, in a dispersive and non-dissipative setting such a solution typically exhibits Gibbs-like high-oscillation and non-vanishing overshoot as t tends to zero. In this talk, I will discuss the explicit solution of general (1+1)-dimensional initial-boundary value problems using the so-called Unified Transform Method, the behavior of corner singularities and their relation to the classical Gibbs phenomenon. I will also discuss the computation of these singular solutions.