Polynomial stabilization of some dissipative hyperbolic systems

Kaïs Ammari , E. Feireisl , Serge Nicaise (1)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

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. Exponential 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.

Domaines: Mathématiques [math]

Kaïs Ammari, E. Feireisl, Serge Nicaise. Polynomial stabilization of some dissipative hyperbolic systems. Discrete and Continuous Dynamical Systems - Series A, 2014, 34 (11), pp.4371-4388. ⟨10.3934/dcds.2014.34.4371⟩. ⟨hal-03138443⟩