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Exponential decay estimates for the damped defocusing Schrödinger equation in exterior domains.
- Source :
-
Journal of Mathematical Physics . Oct2023, Vol. 64 Issue 10, p1-32. 32p. - Publication Year :
- 2023
-
Abstract
- We are concerned with the existence as well as the exponential stability in H1-level for the damped defocusing Schrödinger equation posed in a two-dimensional exterior domain Ω with smooth boundary ∂Ω. The proofs of the existence are based on the properties of pseudo-differential operators introduced in Dehman et al. [Math. Z. 254, 729–749 (2006)] and a Strichartz estimate proved by Anton [Bull. Soc. Math. Fr. 136, 27–65 (2008)], while the exponential stability is achieved by combining arguments firstly considered by Zuazua [J. Math. Pures Appl. 9, 513–529 (1991)] for the wave equation adapted to the present context and a global uniqueness theorem. In addition, we proved propagation results for the linear Schrödinger equation for any dimensional and for any (reasonable) boundary conditions employing microlocal analysis. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 64
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 173336107
- Full Text :
- https://doi.org/10.1063/5.0101506