Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 1088-1096.

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The PDP Feedback Control and Stability Analysis of a Diffusive Wave Equation

Dongxia Fan(),Dongxia Zhao*(),Na Shi(),Tingting Wang()   

  1. School of Science, North University of China, Taiyuan 030051
  • Received:2020-09-24 Online:2021-08-26 Published:2021-08-09
  • Contact: Dongxia Zhao;;;
  • Supported by:
    the NSFC(61603351);the NSF of Shanxi Province(201801D121027);the NSF of Shanxi Province(201701-D221121);the 17th Postgraduate Science and Technology Project of The North University of China(20201747)


In this paper, a position and delayed position (PDP) feedback controller is established for the Hayami diffusive wave equation. The well-posedness of the closed system is studied firstly, and then, by the method of Lyapunov function, the exponential stability is obtained. Finally, compared with the previous results, the range of the control parameters is expanded in this paper, which shows the efficiency and feasibility of PDP feedback.

Key words: Diffusive wave equation, PDP feedback, Lyapunov function, Exponential stability

CLC Number: 

  • O231.4