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Indirect stabilization of hyperbolic systems through resolvent estimates

Abstract : We prove a sharp decay rate for the total energy of two classes of systems of weakly coupled hyperbolic equations. We show that we can stabilize the full system through a single damping term, acting on one component only of the system (indirect stabilization). The energy estimate is achieved by means of suitable estimates of the resolvent operator norm. We apply this technique to a system of wave-wave equation and to a wave-Petrovsky system.
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https://hal.inria.fr/hal-01101269
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Submitted on : Thursday, January 8, 2015 - 11:31:35 AM
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Roberto Guglielmi. Indirect stabilization of hyperbolic systems through resolvent estimates. 2014. ⟨hal-01101269⟩

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