Boundary Stabilization of Heat Equation with Multi-Point Heat Source

Qing-Qing Hu, Feng-Fei Jin and Bao-Qiang Yan
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Qing-Qing Hu: School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
Feng-Fei Jin: School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
Bao-Qiang Yan: School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China

Mathematics, 2021, vol. 9, issue 8, 1-20

Abstract: In this paper, we consider boundary stabilization problem of heat equation with multi-point heat source. Firstly, a state feedback controller is designed mainly by backstepping approach. Under the designed state controller, the exponential stability of closed-loop system is guaranteed. Then, an observer-based output feedback controller is proposed. We prove the exponential stability of resulting closed-loop system using operator semigroup theory. Finally, the designed state and output feedback controllers are effective via some numerical simulations.

Keywords: boundary stabilization; heat equation; multi-point heat source; backstepping transformation; parabolic equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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