Variational approximation methods for eigenvalues. Convergence theorems
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Variational characterization of eigenvalues of a non-symmetric eigenvalue problem governing elastoacoustic vibrations
Markus Stammberger, Heinrich Voss (2014)
Applications of Mathematics
Small amplitude vibrations of an elastic structure completely filled by a fluid are considered. Describing the structure by displacements and the fluid by its pressure field one arrives at a non-selfadjoint eigenvalue problem. Taking advantage of a Rayleigh functional we prove that its eigenvalues can be characterized by variational principles of Rayleigh, minmax and maxmin type.
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