Astronomy and Astrophysics – Astrophysics
Scientific paper
Sep 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976ap%26ss..44..177p&link_type=abstract
Astrophysics and Space Science, vol. 44, Sept. 1976, p. 177-215. Research supported by the Fonds National de la Recherche Scien
Astronomy and Astrophysics
Astrophysics
6
Differential Equations, Dynamic Stability, Hydrodynamic Equations, Stellar Models, Stellar Structure, Eigenvalues, Eigenvectors, Function Space, Stellar Evolution, Thermodynamics
Scientific paper
A formalism is presented for investigating local stellar stability in terms of ordinary differential equations. Local stability is defined as being related to continuous branches of eigenvalues expressible as functions of position in the star, and a systematic approach is outlined for tracing these continuous branches. Attention is focused on stellar situations where the partial differential eigenvalue problem can be reduced to a system of ordinary differential equations. Distributions in a generalized function space and superregularizations are evaluated as solutions to the differential system, and it is shown that the introduction of superregularizations allows continuous branches of eigenvalues to be associated with all spectral equations defining linear stellar stability in radial as well as nonradial dynamical, vibrational, and secular stability problems. The present approach is illustrated by short analyses of the radial and nonradial dynamical stability problems.
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