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Bounds for the spectrum of a matrix differential operator with a damping term

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Abstract

We consider a second-order matrix ordinary regular differential nonselfadjoint operator with a damping term and selfadjoint boundary conditions. An estimate for the resolvent and bounds for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.

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  1. Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, 84105, Beer-Sheva, Israel

    M. I. Gil’

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  1. M. I. Gil’
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Correspondence to M. I. Gil’.

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Gil’, M.I. Bounds for the spectrum of a matrix differential operator with a damping term. Z. Angew. Math. Phys. 62, 87–97 (2011). https://doi.org/10.1007/s00033-010-0077-0

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  • DOI: https://doi.org/10.1007/s00033-010-0077-0

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