In this paper we study the asymptotic dynamics for semilinear defocusing Schrödinger equation subject to a damping locally distributed on a n-dimentional compact Riemannian manifold M n without boundary. The proofs are based on a result of unique continuation property, in the construction of a function f whose Hessian is positive definite and ∆f = C 0 in some region contained in M and about the smoothing effect due to Aloui adapted to the present context.
This paper is concerned with a 2-dimensional Klein-Gordon-Schrödinger system subject to two types of locally distributed damping on a compact Riemannian manifold without boundary. Making use of unique continuation property, the observability inequalities, and the smoothing effect due to Aloui, we obtain exponential stability results.
KEYWORDScompact manifolds, differential equations on manifolds, exponential stability, Klein-Gordon-Schrödinger system MSC CLASSIFICATION 35L70; 35B40
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