Polynomial stabilization of some dissipative hyperbolic systems
Analysis of PDEs
2012-08-23 v1
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.
Cite
@article{arxiv.1208.4485,
title = {Polynomial stabilization of some dissipative hyperbolic systems},
author = {K. Ammari and E. Feireisl and S. Nicaise},
journal= {arXiv preprint arXiv:1208.4485},
year = {2012}
}