Indirect stabilization of weakly coupled systems with hybrid boundary conditions
Fatiha Alabau-Boussouira - Present position Délégation CNRS at MAPMO, UMR 6628, Current position Université Paul Verlaine-Metz, Ile du Saulcy, 57045 Metz Cedex 1, France (email)
Abstract: 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.
Keywords: Indirect stabilization, energy estimates, interpolation spaces, evolution equations, hyperbolic systems.
Received: March 2011; Revised: July 2011; Published: November 2011.