Polynomial stabilization of some dissipative hyperbolic systems

0429223 - MÚ 2015 RIV US eng J - Článek v odborném periodiku
Ammari, K. - Feireisl, Eduard - Nicaise, S.
Polynomial stabilization of some dissipative hyperbolic systems.
Discrete and Continuous Dynamical Systems. Roč. 34, č. 11 (2014), s. 4371-4388. ISSN 1078-0947. E-ISSN 1553-5231
Grant CEP: GA ČR GA201/09/0917
Institucionální podpora: RVO:67985840
Klíčová slova: exponential stability * polynomial stability * observability inequality
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.972, rok: 2014
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=9924

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 veri ed 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.
Trvalý link: http://hdl.handle.net/11104/0234368