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Spectral Analysis of an Operator Arising in Fluid Dynamics

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Eigenmode solutions are very important in stability analysis of dynamical systems. The set of eigenvalues of a non-self-adjoint differential operator originated from the linearization of some Cauchy problem is investigated. It is shown that the eigenvalues are purely imaginary, and that they are related to the eigenvalues of Heun's differential equation. These two results are used to derive the asymptotic behavior of the eigenvalues and to compute them numerically.
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Document Type: Research Article

Affiliations: 1: University of Toronto 2: University of Wisconsin at Milwaukee

Publication date: October 1, 2009

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