Polynomial stabilization of some dissipative hyperbolic systems

K. Ammari; E. Feireisl; S. Nicaise

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arXiv · 1208.4485

Polynomial stabilization of some dissipative hyperbolic systems

K. Ammari·E. Feireisl·S. Nicaise

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Abstract

We study the problem of stabilization for the acoustic system with a spatially distributed damping. Imposing various hypotheses on the structural properties of the damping term, we identify either exponential or polynomial decay of solutions with growing time. Expo- nential decay rate is shown by means of a time domain approach, reducing the problem to an observability inequality to be verified for solutions of the associated conservative problem. In addition, we show a polynomial stabilization result, where the proof uses a frequency domain method and combines a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent.

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K. Ammari, E. Feireisl, S. Nicaise. 2012-08-22. Polynomial stabilization of some dissipative hyperbolic systems. https://arxiv.org/abs/1208.4485

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