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Journal of Systems Science and Complexity

, Volume 31, Issue 4, pp 889–906 | Cite as

Control and Stabilization of the Rosenau Equation Posed on a Periodic Domain

  • Deqin Zhou
  • Chunlai Mu
Article
  • 93 Downloads

Abstract

This paper considers the Rosenau equation with a moving control
$${\partial _t}u + {\partial _t}\partial _x^4u + {\partial _x}u + u{\partial _x}u = a(x + ct)h(x,t),c \ne 0,x \in T = \mathbb{R}/(2\pi \mathbb{Z}),t > 0$$
. The authors prove that the Rosenau equation with a moving control is locally exact controllable in H s (T) with s ≥ 0 and globally exponential stable in H s (T) with s ≥ 2. The two results nontrivially extend the work of (Rosier L and Zhang B Y, 2013) from the BBM equation to the Rosenau equation.

Keywords

Exact controllability Rosenau equation stabilization 

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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsChongqing UniversityChongqingChina

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