The University of Arizona

Old and new bounds on solutions of the Helmholtz equation proved by integrating by parts

Analysis, Dynamics, and Applications Seminar

Old and new bounds on solutions of the Helmholtz equation proved by integrating by parts
Series: Analysis, Dynamics, and Applications Seminar
Location: Hybrid: Math 402/Online
Presenter: Euan Spence, Department of Mathematical Sciences, University of Bath, United Kingdom

A classic technique in PDE theory is that of multiplying by a carefully-chosen test function and integrating by parts. This method was famously used to prove bounds on the Helmholtz equation in the 1960s and 1970s by Cathleen Morawetz. Much-more sophisticated methods now exist for proving bounds on the Helmholtz equation, but (perhaps surprisingly) the multiplier method can still be used to prove new results. In this talk I will review the classic multiplier method, and then discuss a recent application of it to Helmholtz problems in the paper "Scattering by finely-layered obstacles: frequency-explicit bounds and homogenization" https://arxiv.org/abs/2109.11267 , co-authored with Th\'eophile Chaumont-Frelet (INRIA, Nice).

Place: Hybrid, Math, 402 and
Zoom: https://arizona.zoom.us/j/81150211038 
Password: “arizona” (all lower case)