Asymptotic separation of the spectrum of quadratic operator pencils associated with damped dynamical systems

Article type: Research Article

Authors: Pivovarchik, Vjacheslav | Tretter, Christiane^;

Affiliations: Department of Higher Mathematics, Odessa State Academy of Civil Engineering and Architecture, Ul. Didrikhsona 4, 65045 Odessa, Ukraine E‐mail: [email protected] | FB3 – Mathematik, University of Bremen, Bibliothekstr. 1, 28359 Bremen, Germany E‐mail: [email protected]‐bremen.de

Note: [] Corresponding author.

Abstract: We investigate the spectrum of a damped quadratic operator pencil with 2×2 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.

Journal: Asymptotic Analysis, vol. 36, no. 1, pp. 1-12, 2003