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Stabilization and control for the biharmonic Schr\"odinger equation. (arXiv:1807.05264v1 [math.AP])
来源于:arXiv
The main purpose of this paper is to show the global stabilization and exact
controllability properties for a fourth order nonlinear fourth order nonlinear
Schr\"odinger system: $$i\partial_tu +\partial_x^2u-\partial_x^4u=\lambda
|u|^2u,$$ on a periodic domain $\mathbb{T}$ with internal control supported on
an arbitrary sub-domain of $\mathbb{T}$. More precisely, by certain properties
of propagation of compactness and regularity in Bourgain spaces, for the
solutions of the associated linear system, we show that the system is globally
exponentially stabilizable. This property together with the local exact
controllability ensures that fourth order nonlinear Schr\"odinger is globally
exactly controllable. 查看全文>>