Abstract
This paper considers the existence of global smooth solutions of semilinear schrödinger equation with a boundary feedback on 2-dimensional Riemannian manifolds when initial data are small. The authors show that the existence of global solutions depends not only on the boundary feedback, but also on a Riemannian metric, given by the coefficient of the principle part and the original metric of the manifold. In particular, the authers prove that the energy of the system decays exponentially.
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This research is supported by the National Science Foundation of China under Grants Nos. 60225003, 60334040, 60221301, 60774025, and 10831007, and Chinese Academy of Sciences under Grant No KJCX3-SYW-S01.
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Deng, L., Yao, P. Global smooth solutions for semilinear Schrödinger equations with boundary feedback on 2-dimensional Riemannian manifolds. J Syst Sci Complex 22, 749–776 (2009). https://doi.org/10.1007/s11424-009-9199-x
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DOI: https://doi.org/10.1007/s11424-009-9199-x