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

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

2008-03-14

arxiv.org/abs/0803.2248v2

Zeitschrift fuer angewandte Mathematik und Physik, 2010, Vol. 61, No. 2, P. 221-234

Physics

Mathematical Physics

17 pages, 4 figures, presented at the International Conference "Modern Analysis and Applications - MAA 2007" dedicated to the

Scientific paper

10.1007/s00033-009-0032-0

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.

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