A general formula for decay rates of nonlinear dissipative systems

Fatiha Alabau-Boussouira (1)

1 LMAM - Laboratoire de Mathématiques et Applications de Metz

This work is concerned with stabilization of hyperbolic systems by a nonlinear feedback which can be localized on part of the boundary or locally distributed. We present here a general formula which gives the energy decay rates in terms of the behavior of the nonlinear feedback close to the origin. This formula allows us to unify for instance the cases where the feedback has a polynomial growth at the origin, with the cases where it goes exponentially fast to zero at the origin. We give also two other significant examples of nonpolynomial growth at the origin. We also show that we either obtain or improve significantly the decay rates of Lasiecka and Tataru (Differential Integral Equations 8 (1993) 507–533) and Martinez (Rev. Mat. Comput. 12 (1999) 251–283). To cite this article: F. Alabau-Boussouira, C. R. Acad. Sci. Paris, Ser. I 338 (2004).

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]; Mathématiques [math]

Fatiha Alabau-Boussouira. A general formula for decay rates of nonlinear dissipative systems. Comptes Rendus. Mathématique, 2004, 338 (1), pp.35-40. ⟨10.1016/j.crma.2003.10.024⟩. ⟨hal-03895190⟩