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Stabilization and asymptotic behavior of a generalized telegraph equation

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Abstract

We analyze the stability of different models of the telegraph equation set in a real interval. They correspond to the coupling between a first-order hyperbolic system and a first-order differential equation of parabolic type. We show that some models have an exponential decay rate, while other ones are only polynomially stable. When the parameters are constant, we show that the obtained polynomial decay is optimal and in the case of an exponential decay that the decay rate is equal to the spectral abscissa. These optimality results are based on a careful spectral analysis of the operator. In particular, we characterize its full spectrum that is made of a discrete set of eigenvalues and an essential spectrum reduced to one point.

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  1. LAMAV, FR CNRS 2956, Institut des Sciences et Techniques of Valenciennes, Université de Valenciennes et du Hainaut Cambrésis, 59313, Valenciennes Cedex 9, France

    Serge Nicaise

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  1. Serge Nicaise
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Nicaise, S. Stabilization and asymptotic behavior of a generalized telegraph equation. Z. Angew. Math. Phys. 66, 3221–3247 (2015). https://doi.org/10.1007/s00033-015-0568-0

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