This paper considers the existence of global smooth solutions of semilinear schrSdinger equation with a boundary feedback on 2-dimensional Riemannian manifolds when initial data are small. The authors show that the ex...This paper considers the existence of global smooth solutions of semilinear schrSdinger 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.展开更多
基金supported by the National Science Foundation of China under Grants Nos. 60225003, 60334040, 60221301, 60774025, and 10831007Chinese Academy of Sciences under Grant No KJCX3-SYW-S01
文摘This paper considers the existence of global smooth solutions of semilinear schrSdinger 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.
