# American Institute of Mathematical Sciences

March  2017, 6(1): 59-75. doi: 10.3934/eect.2017004

## Indirect stabilization of hyperbolic systems through resolvent estimates

 Radon Institute for Computational and Applied Mathematics - RICAM, Altenbergerstraße 69, 4040 - Linz, Austria

Received  February 2015 Revised  September 2016 Published  December 2016

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, in feedback form, acting on one component only of the system (\emph{indirect stabilization}). The energy estimate is achieved by means of suitable estimates of the resolvent operator norm. We apply this technique to a wave-wave system and to a wave-Petrovsky system.

Citation: Roberto Guglielmi. Indirect stabilization of hyperbolic systems through resolvent estimates. Evolution Equations & Control Theory, 2017, 6 (1) : 59-75. doi: 10.3934/eect.2017004
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##### References:
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