Abstract
We consider a two-dimensional analog of Helmholtz resonator with walls of finite thickness in the critical case when there exists an eigenfrequency which is the limit of poles generated by both the bounded component of the resonator and the narrow connecting channel. Under the assumption that the limit eigenfrequency is a simple eigenfrequency of the bounded component, the asymptotics of two poles converging to this eigenfrequency are constructed by using the method of matching asymptotic expansions. Explicit formulas for the leading terms of the asymptotics of poles and of the solution of the scattering problem are obtained.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Comptes Rendus de l'Academie des Sciences Series IIB Mechanics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
