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Perturbation of multiparameter non-self-adjoint boundary eigenvalue problems for operator matrices

Kirillov, O. N. (2010):
Perturbation of multiparameter non-self-adjoint boundary eigenvalue problems for operator matrices.
61, In: Zeitschrift fuer angewandte Mathematik und Physik, (2), pp. 221-234, [Article]

Item Type: Article
Erschienen: 2010
Creators: Kirillov, O. N.
Title: Perturbation of multiparameter non-self-adjoint boundary eigenvalue problems for operator matrices
Language: English
Journal or Publication Title: Zeitschrift fuer angewandte Mathematik und Physik
Volume: 61
Number: 2
Divisions: 16 Department of Mechanical Engineering > Dynamics and Vibrations
16 Department of Mechanical Engineering
Date Deposited: 19 Sep 2012 14:21
Identification Number: doi:10.1007/s00033-009-0032-0
Alternative Abstract:
Alternative abstract Language
We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on the complex spectral parameter and on the vector of real physical parameters. We study perturbations of semi-simple multiple eigenvalues as well as perturbations of non-derogatory eigenvalues under small variations of the parameters. Explicit formulae describing the bifurcation of the eigenvalues are derived. Application to the problem of excitation of unstable modes in rotating continua such as spherically symmetric MHD alpha2-dynamo and circular string demonstrates the efficiency and applicability of the theory. Comment: 17 pages, 4 figures, presented at the International Conference "Modern Analysis and Applications - MAA 2007" dedicated to the centenary of Mark Krein. Odessa, Ukraine, April 9-14, 2007. Minor typos correctedEnglish
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