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arXiv · 2210.09130

Exact controllability and stabilization for linear dispersive PDE's on the two-dimensional torus

Francisco J. Vielma Leal·Ademir Pastor
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Abstract

The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE's posed on the two-dimensional torus $\mathbb{T}^{2}.$ The control function is considered to be acting on a small vertical and horizontal strip of the torus. Our results apply to several well-known models including some bidimesional extensions of the Benajamin-Ono and Korteweg-de Vries equations. As a by product, the exponential stabilizability with any given decay rate is also established in $H^{s}_{p}(\mathbb{T}^{2}),$ with $s\geq 0,$ by constructing an appropriated feedback control law.

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Francisco J. Vielma Leal, Ademir Pastor. 2022-10-17. Exact controllability and stabilization for linear dispersive PDE's on the two-dimensional torus. https://arxiv.org/abs/2210.09130

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