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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on decay rates for Schrödinger's equation


Authors: Jian Xie, Linzi Zhang and Thierry Cazenave
Journal: Proc. Amer. Math. Soc. 138 (2010), 199-207
MSC (2000): Primary 35Q55
Published electronically: August 19, 2009
MathSciNet review: 2550184
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Abstract: We prove the existence of solutions of the Schrödinger equation on $ \mathbb{R}^N$ which decay, in various $ L^p$ spaces, at different rates along different time sequences going to infinity. We establish a similar result for a nonlinear Schrödinger equation.


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Additional Information

Jian Xie
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, 310058, People’s Republic of China
Email: sword711@gmail.com

Linzi Zhang
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, 310058, People’s Republic of China
Email: linzi0116@gmail.com

Thierry Cazenave
Affiliation: Université Pierre et Marie Curie & CNRS, Laboratoire Jacques-Louis Lions, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France
Email: thierry.cazenave@upmc.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10049-7
PII: S 0002-9939(09)10049-7
Keywords: Schr\"odinger's equation, asymptotic behavior, decay rate
Received by editor(s): March 3, 2009
Published electronically: August 19, 2009
Additional Notes: The first two authors were supported by NSFC 10871175
Communicated by: Walter Craig
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.