Asymptotic Stability for the Damped Schrodinger Equation on Noncompact Riemannian Manifolds and Exterior Domains

作者：Bortot Cesar A; Cavalcanti Marcelo M^*

来源：Communications in Partial Differential Equations, 2014, 39(9): 1791-1820.

DOI：10.1080/03605302.2014.908390

• Exponential stability
• Non-compact manifolds
• Schroedinger equation

The Schrodinger equation subject to a nonlinear and locally distributed damping, posed in a connected, complete, and noncompact n dimensional Riemannian manifold (M,g) is considered. Assuming that (M, g) is nontrapping and, in addition, that the damping term is effective in M\Omega, where Omega subset of subset of M is an open bounded and connected subset with smooth boundary partial derivative Omega, such that (Omega) over bar is a compact set, exponential and uniform decay rates of the L-2-level energy are established. The main ingredients in the proof of the exponential stability are: (A) an unique continuation property for the linear problem; and (B) a local smoothing effect for the linear and nonhomogeneous associated problem.

• 出版日期2014