Volume 24, Number 2, April–June 2018
|Page(s)||519 - 549|
|Published online||26 January 2018|
Energy decay in a wave guide with dissipation at infinity
Laboratoire de Mathématique: Modélisation Déterministe et Aléatoire (LAMMDA), École Supérieure des Sciences et de la Technologie de Hammam Sousse, Université de Sousse,
Rue Lamine Abassi,
2 Institut de Mathématiques de Toulouse, Université Toulouse 3, 118 route de Narbonne, 31062 Toulouse Cedex 9, France
a Corresponding author: email@example.com
Revised: 1 June 2017
Accepted: 12 August 2017
We prove local and global energy decay for the wave equation in a wave guide with damping at infinity. More precisely, the absorption index is assumed to converge slowly to a positive constant, and we obtain the diffusive phenomenon typical for the contribution of low frequencies when the damping is effective at infinity. On the other hand, the usual Geometric Control Condition is not necessarily satisfied so we may have a loss of regularity for the contribution of high frequencies. Since our results are new even in the Euclidean space, we also state a similar result in this case.
Mathematics Subject Classification: 35L05 / 35J10 / 35J25 / 35B40 / 47A10 / 47B44
Key words: Local and global energy decay / dissipative wave equation / wave guides / diffusive phenomenon / semiclassical analysis / low frequency resolvent estimates
© EDP Sciences, SMAI 2018
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