Exponential decay for the Schrödinger equation on a dissipative waveguide

Julien Royer (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We prove exponential decay for the solution of the Schrödinger equation on a dissipative waveguide. The absorption is effective everywhere on the boundary but the geometric control condition is not satisfied. The proof relies on separation of variables and the Riesz basis property for the eigenfunctions of the transverse operator. The case where the absorption index takes negative values is also discussed.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Julien Royer. Exponential decay for the Schrödinger equation on a dissipative waveguide. Annales Henri Poincaré, 2015, 16 (8). ⟨hal-00954688v2⟩