Rate of decay of some Petrowsky-like dissipative systems

Kais Ammari (1) , Mouez Dimassi (2) , Maher Zerzeri (3)

1 FSM - Faculté des Sciences de Monastir
2 IMB - Institut de Mathématiques de Bordeaux
3 LAGA - Laboratoire Analyse, Géométrie et Applications

In this paper, we show that the fastest decay rate for some Petrowsky-like dissipative systems is given by the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup, if the corresponding operator satisfied some spectral gap condition. We give also some applications to illustrate our setting.

Mots clés: Riesz Basis; Rate of Decay; Petrowsky-like systems; Spectral Abscissa; Riesz Basis.

Domaines: Equations aux dérivées partielles [math.AP]

Kais Ammari, Mouez Dimassi, Maher Zerzeri. Rate of decay of some Petrowsky-like dissipative systems. 2014. ⟨hal-01018784v2⟩