Global exact controllability to the trajectories of the Kuramoto-Sivashinsky equation

Peng Gao

doi:10.3934/eect.2020002

Article Contents

2020, Volume 9, Issue 1: 181-191. Doi: 10.3934/eect.2020002

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Global exact controllability to the trajectories of the Kuramoto-Sivashinsky equation

Peng Gao^1,2, ,

1.
State Key Laboratory of Automotive Simulaion and Control, Jilin University, Changchun 130012, China
2.
School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, China

^* Corresponding author: Peng Gao
^* Corresponding author: Peng Gao

Received: September 30, 2018

Revised: February 28, 2019

Early access: August 2019

Published: March 2020

This work is supported by Foundation of State Key Laboratory of Automotive Simulation and Control and NSFC Grant (11601073)

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Abstract

In this paper, we establish the global exact controllability to the trajectories of the Kuramoto-Sivashinsky equation by five controls: one control is the right member of the equation and is constant with respect to the space variable, the four others are the boundary controls.

Keywords:

Global exact controllability,
Kuramoto-Sivashinsky equation.

Mathematics Subject Classification: Primary: 93B05; Secondary: 35K55.

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References

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