✦ LIBER ✦

Resonance phenomena for a class of partial differential equations of higher order in cylindrical waveguides

✍ Scribed by P. Lesky Jr.; P. Werner

Publisher: John Wiley and Sons
Year: 1989
Tongue: English
Weight: 907 KB
Volume: 11
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1670110601

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✦ Synopsis

Communicated by P. Werner

We consider a domain f2 in R" of the form R = R' x R' with bounded R' c W-'. In f2 we study the Dirichlet initial and boundary value problem for the equation a t u + [(-a: -. . . -a:)"'+, (-a:+l -* . * -aX)"]u = fe-'"I. We show that resonances can occur if 2m 3 1. In particular, the amphtude of u may increase like t' (a rational, 0 < a < 1) or like In t as t + 03. Furthermore, we prove that the limiting amplitude principle holds in the remaining cases.

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