Local energy decay and smoothing effect for the damped Schr{ö}dinger equation

Abstract

We prove the local energy decay and the smoothing effect for the damped Schr{ö}dinger equation on R^d. 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 which we consider.

References in corpus (6)

• Carleman estimates and absence of embedded eigenvalues
• Limiting absorption principle for the dissipative Helmholtz equation
• Local Energy Decay for the Damped Wave Equation
• Exponential decay for the Schr{ö}dinger equation on a dissipative waveguide
• Sharp low frequency resolvent estimates on asymptotically conical manifolds
• Mourre's method for a dissipative form perturbation