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Boundary Stabilization of Heat Equation with Multi-Point Heat Source

Author

Listed:
  • 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)

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.

Suggested Citation

  • Qing-Qing Hu & Feng-Fei Jin & Bao-Qiang Yan, 2021. "Boundary Stabilization of Heat Equation with Multi-Point Heat Source," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:834-:d:534277
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    References listed on IDEAS

    as
    1. Sachin Kumar & Jinde Cao & Xiaodi Li, 2020. "A Numerical Method for Time-Fractional Reaction-Diffusion and Integro Reaction-Diffusion Equation Based on Quasi-Wavelet," Complexity, Hindawi, vol. 2020, pages 1-11, September.
    2. Kumar, Sachin & Pandey, Prashant, 2020. "Quasi wavelet numerical approach of non-linear reaction diffusion and integro reaction-diffusion equation with Atangana–Baleanu time fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
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