Indirect stabilization of weakly coupled systems with hybrid boundary conditions

Fatiha Alabau-Boussouira (1, 2) , Piermarco Cannarsa (3) , Roberto Guglielmi (3)

1 LMAM - Laboratoire de Mathématiques et Applications de Metz
2 CORIDA - Robust control of infinite dimensional systems and applications
3 DIPMAT - Dipartimento di Matematica [Roma II]

We investigate stability properties of indirectly damped systems of evolution equations in Hilbert spaces, under new compatibility assumptions. We prove polynomial decay for the energy of solutions and optimize our results by interpolation techniques, obtaining a full range of power-like decay rates. In particular, we give explicit estimates with respect to the initial data. We discuss several applications to hyperbolic systems with hybrid boundary conditions, including the coupling of two wave equations subject to Dirichlet and Robin type boundary conditions, respectively.

Mots clés: indirect stabilization; interpolation spaces; energy estimates; evolution equations; hyperbolic systems

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]; Algèbres d'opérateurs [math.OA]

Fatiha Alabau-Boussouira, Piermarco Cannarsa, Roberto Guglielmi. Indirect stabilization of weakly coupled systems with hybrid boundary conditions. 2011. ⟨hal-00601281⟩