Analysis & PDE
- Anal. PDE
- Volume 10, Number 6 (2017), 1285-1315.
Local energy decay and smoothing effect for the damped Schrödinger equation
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.
Anal. PDE, Volume 10, Number 6 (2017), 1285-1315.
Received: 3 June 2015
Revised: 14 March 2017
Accepted: 24 April 2017
First available in Project Euclid: 16 November 2017
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Zentralblatt MATH identifier
Primary: 35B40: Asymptotic behavior of solutions 35Q41: Time-dependent Schrödinger equations, Dirac equations 35B65: Smoothness and regularity of solutions 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] 47B44: Accretive operators, dissipative operators, etc.
Khenissi, Moez; Royer, Julien. Local energy decay and smoothing effect for the damped Schrödinger equation. Anal. PDE 10 (2017), no. 6, 1285--1315. doi:10.2140/apde.2017.10.1285. https://projecteuclid.org/euclid.apde/1510843524