The University of Arizona: Old and New Bounds on Solutions of the Helmholtz Equation Proved by Integrating by Parts
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).
Series: Analysis, Dynamics, and Applications Seminar
Hybrid: Math 402/Online
Presenter: Euan Spence, Department of Mathematical Sciences, University of Bath, United Kingdom
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