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Local energy decay
and smoothing effect for the damped Schrödinger equation
Moez Khenissi and Julien Royer |
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Vol. 10 (2017), No. 6, 1285–1315
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Abstract |
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We prove the local energy decay and the global smoothing effect for the damped Schrödinger equation on . The self-adjoint part is a Laplacian associated to a long-range perturbation of the flat metric. The proofs are based on uniform resolvent estimates obtained by the dissipative Mourre method. All the results depend on the strength of the dissipation that we consider. |
Keywords
local energy decay, smoothing effect, damped Schrödinger
equation, resolvent estimates
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Mathematical Subject Classification 2010
Primary: 35B40, 35Q41, 35B65, 47A55, 47B44
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Milestones
Received: 3 June 2015
Revised: 14 March 2017
Accepted: 24 April 2017
Published: 14 July 2017
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Authors |
| Moez Khenissi | |
| LAMMDA École Supérieure des Sciences et de Technologie de Hammam Sousse Université de Sousse Rue Lamine El Abbessi 4011 Hammam Sousse Tunisia |
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| Julien Royer | |
| Institut de Mathématiques de
Toulouse 118, route de Narbonne 31062 Toulouse Cédex 9 France |
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