Special Colloquium
Speaker: Pu Zhao Kow, National Chengchi University
Host: Suman Kumar Sahoo
Title: On scattering behavior of corner domains with anisotropic inhomogeneities
Time, day and date: 3:00:00 PM – 4:00:00 PM, Wednesday, September 09
Venue: Ramanujan Hall

Video Call: https://meet.google.com/ztk-bwit-ioy

Abstract: We investigate the scattering and non-scattering behavior of an anisotropic, inhomogeneous Lipschitz medium at a fixed wave number under a single incident field. By relating the anisotropic non-scattering problem to a Bernoulli-type free boundary problem, we leverage techniques from free boundary theory to show that any anisotropic medium with a Lipschitz, but not C1,α, boundary scatters all incident waves satisfying a non-degeneracy condition [1]. For degenerate incident waves, the outcomes fall into two categories [2]: In the first, we show that in two dimensions, piecewise C1 or convex penetrable obstacles with corners (and in higher dimensions, obstacles with edge points) always produce nontrivial scattering. In the second, we prove that piecewise C 1 obstacles with corners in two dimensions (or with edge points in higher dimensions) whose angles are not rational multiples also generate nontrivial scattering for any incoming wave. This is a joint work with Mikko Salo and Henrik Shahgholian.