local energy decay;
smoothing effect;
damped Schrodinger equation;
resolvent estimates;
WAVE-EQUATION;
EXPONENTIAL DECAY;
EXTERIOR;
STABILIZATION;
ABSENCE;
REGULARITY;
RESOLVENT;
D O I:
10.2140/apde.2017.10.1285
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
We prove the local energy decay and the global smoothing effect for the damped Schrodinger equation on R-d. The self-adjoint part is a Laplacian associated to a long-range perturbation of the flat metric. The proofs are based on uniform resolvent estimates obtained by the dissipative Mourre method. All the results depend on the strength of the dissipation that we consider.