Eigenvalue bifurcation in multiparameter families of non-self-adjoint operator matrices

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Abstract

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 p. We study perturbations of semi-simple multiple eigenvalues as well as perturbations of non-derogatory eigenvalues under small variations of p. 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 alpha-alpha-dynamo and circular string demonstrates the efficiency and applicability of the approach.
Original languageEnglish
Pages (from-to)221-234
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume61
Issue number2
Early online date15 Aug 2009
DOIs
Publication statusPublished - Apr 2010

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