Locating real eigenvalues of a spectral problem in fluid-solid type structures.

Voss, Heinrich

Displaying similar documents to “Locating real eigenvalues of a spectral problem in fluid-solid type structures.”

A maxmin principle for nonlinear eigenvalue problems with application to a rational spectral problem in fluid-solid vibration

Heinrich Voss (2003)

Applications of Mathematics

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In this paper we prove a maxmin principle for nonlinear nonoverdamped eigenvalue problems corresponding to the characterization of Courant, Fischer and Weyl for linear eigenproblems. We apply it to locate eigenvalues of a rational spectral problem in fluid-solid interaction.

Variational characterization of eigenvalues of a non-symmetric eigenvalue problem governing elastoacoustic vibrations

Markus Stammberger, Heinrich Voss (2014)

Applications of Mathematics

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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.

On a class of nonlinear eigenvalue problems

Karl P. Hadeler (1974)

Acta Universitatis Carolinae. Mathematica et Physica

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Equality in Wielandt’s eigenvalue inequality

Shmuel Friedland (2015)

Special Matrices

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In this paper we give necessary and sufficient conditions for the equality case in Wielandt’s eigenvalue inequality.

Dependence of a differential equation on the first eigenvalue of a suitable problem

Jan Bochenek (1980)

Annales Polonici Mathematici

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On some properties of eigenvalues and eigenfunctions of certain differential equations of the fourth order

Jan Bochenek (1971)

Annales Polonici Mathematici

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A new method for obtaining eigenvalues of variational inequalities. Branches of eigenvalues of the equation with the penalty in a special case

Milan Kučera (1979)

Časopis pro pěstování matematiky

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Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems

J. Fleckinger, J. Hernández, F. Thélin (2004)

Bollettino dell'Unione Matematica Italiana

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We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.