Optimal lower bound of the resonance widths for the Helmholtz Resonator

2014/02/26 by Martinez André, André, Martinez, Nédélec Laurence +1
Computer Science · Engineering · Mathematics · #35B34 #35P15 #81Q20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations #math.AP #msc:35B34 #msc:35P15 #msc:81Q20

paper · pdf · doi:10.48550/arxiv.1402.6493

25 pages, 2 figures

openalex publication_date 2014/02/26 · arxiv created 2015/02/09 · arxiv updated 2015/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Under a geometric assumption on the region near the end of its neck, we prove an optimal exponential lower bound on the widths of resonances for a general two-dimensional Helmholtz resonator. An extension of the result to the n-dimensional case, n smaller than 12, is also obtained.

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