Two simple criterion to obtain exact controllability and stabilization of a linear family of Dispersive PDE's on a periodic domain

Francisco J. Vielma Leal; Ademir Pastor

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arXiv · 2110.02086

Two simple criterion to obtain exact controllability and stabilization of a linear family of Dispersive PDE's on a periodic domain

Francisco J. Vielma Leal·Ademir Pastor

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Abstract

In this work, we use the classical moment method to find a practical and simple criterion to determine if a family of linearized Dispersive equations on a periodic domain is exactly controllable and exponentially stabilizable with any given decay rate in $H^{s}_{p}(\mathbb{T})$ with $s\in \mathbb{R}$. We apply these results to prove that the linearized Smith equation, the linearized dispersion-generalized Benjamin-Ono equation, the linearized fourth-order Schr\"odinger equation, and the Higher-order Schr\"odinger equations are exactly controllable and exponentially stabilizable with any given decay rate in $H^{s}_{p}(\mathbb{T})$ with $s\in \mathbb{R}$.

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Francisco J. Vielma Leal, Ademir Pastor. 2021-10-05. Two simple criterion to obtain exact controllability and stabilization of a linear family of Dispersive PDE's on a periodic domain. https://arxiv.org/abs/2110.02086

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