Speaker

Professor André Martinez, Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 40126 Bologna, Italy  

　　Title

Optimal estimates on the width of resonances for a Helmholtz resonator (I)

　　Time

　　Venue

Morningside 410

　　Abstract

We consider a 2 dimensional Helmholtz resonator consisting of a cavity connected to an exterior domain through a thin tube. Under a geometric assumption on the end part of this tube, we prove an optimal exponential lowe
r bound on the widths of the resonances as the size of the tube's section goes to zero. An extension to larger dimensions is obtained, too.
The proof is based on Carleman estimates up to the boundary, and on connection formulas at the contact region between the tube and the exterior domain. This is a joint work with L. Nédélec. 

　　Affiliation