Annales Henri Poincaré

, Volume 16, Issue 8, pp 1807–1836 | Cite as

Exponential Decay for the Schrödinger Equation on a Dissipative Waveguide

  • Julien RoyerEmail author


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.


Absorption Index Exterior Domain Riesz Basis Dissipative Operator Resolvent Estimate 
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© Springer Basel 2014

Authors and Affiliations

  1. 1.Institut de Mathématiques de ToulouseToulouse Cédex 09France

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