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

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• Euan Spence (University of Bath)
• Monday 28 February 2022, 15:00-16:00
• Zoom.

If you have a question about this talk, please contact Alistair Hales.

A classic technique to study PDEs 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 Theophile Chaumont-Frelet (INRIA, Nice).

This talk is part of the Waves Group (DAMTP) series.

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