A general method for proving sharp energy decay rates for memory-dissipative evolution equations |
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Authors: | Fatiha Alabau-Boussouira Piermarco Cannarsa |
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Institution: | 1. L.M.A.M. CNRS-UMR 7122 et INRIA Équipe-projet CORIDA, université Paul-Verlaine-Metz, Ile du Saulcy, 57045 Metz cedex 01, France;2. Dipartimento di Matematica, Università di Roma Tor Vergata, 00133 Roma, Italy |
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Abstract: | This Note is concerned with stabilization of hyperbolic systems by a distributed memory feedback. We present here a general method which gives energy decay rates in terms of the asymptotic behavior of the kernel at infinity. This method, which allows us to recover in a natural way the known cases (exponential, polynomial, …), applies to a large quasi-optimal class of kernels. It also provides sharp energy decay rates compared to the ones that are available in the literature. We give a general condition under which the energy of solutions is shown to decay at least as fast as the kernel at infinity. To cite this article: F. Alabau-Boussouira, P. Cannarsa, C. R. Acad. Sci. Paris, Ser. I 347 (2009). |
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