IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i8p834-d534277.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/8/834/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/8/834/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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).
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stamov, Gani & Stamova, Ivanka & Martynyuk, Anatoliy & Stamov, Trayan, 2021. "Almost periodic dynamics in a new class of impulsive reaction–diffusion neural networks with fractional-like derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:834-:d:534277. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.