Zero resonances in local perturbations of parallel-plane waveguides

✍ Scribed by P. Werner

• Book ID: 102947080
• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 989 KB
• Volume: 13
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670130203

✦ Synopsis

Abstract

In a joint paper with K. Morgenröther [9] we have studied the propagation of scalar waves in domains of the type Ω = Ω~o~−B̄ with Ω~o~:=ℝ^2^ × (0, 1), where B is a smooth bounded domain with B̄ ⊏ Ω~o~. In particular, we have shown that the solution of Neumann's initial and boundary value problem for the wave equation with time‐independent right‐hand side ƒ increases with a logarithmic rate as t → ∞ if the integral over ƒ does not vanish. The main purpose of the present paper is to extend this result to arbitrary smooth local perturbations of Ω~o~.