THE SPECTRUM OF SOME QUADRATIC OPERATOR PENCILS ASSOCIATED WITH DAMPED DYNAMICAL SYSTEMS


CHRISTIANE TRETTER

ctretter@math.uni-bremen.de

FB 3 - Mathematik
Universität Bremen
Bibliothekstrasse 1
D-28359 Bremen, Germany






We investigate the spectrum of a damped quadratic operator pencil with $ 2 \times 2$ block operator matrix coefficients. Our main result is that the spectrum splits asymptotically into four branches of eigenvalues and we determine their asymptotic behaviour. An application to the vibrations of two interacting connected strings and beams is given where one of them is damped.

(joint work V. Pivovarchik, Odessa)


EPSRC Gregynog Workshop, 21-26 July 2002

Gregynog Abstracts