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What is Asymptotic Behavior of Damped Schrödinger Equations about?

This document discusses the asymptotic behavior of cubic defocusing and damped nonlinear Schrödinger equations on compact Riemannian manifolds without boundary. It establishes that under certain conditions, the energy functional of the solutions decays to zero over time, with stronger damping leading to exponential decay. The results are supported by various mathematical theorems and assumptions related to the geometric control condition and unique continuation properties.

Author

Isnaldo Isaac

Language

EN