Two simple criterion to obtain exact controllability and stabilization of a linear family of Dispersive PDE's on a periodic domain
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 Schrödinger equation, and the Higher-order Schrödinger equations are exactly controllable and exponentially stabilizable with any given decay rate in $H^{s}_{p}(\mathbb{T})$ with $s\in \mathbb{R}$.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2021
- DOI:
- 10.48550/arXiv.2110.02086
- arXiv:
- arXiv:2110.02086
- Bibcode:
- 2021arXiv211002086V
- Keywords:
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- Mathematics - Analysis of PDEs