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Asymptotic Behavior Analysis of a Heat Equation Coupled with a Fractional Ordinary Differential System

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  • Control Theory and Applications
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Abstract

This paper considers the existence, uniqueness and the asymptotic behavior of a classic heat equation coupled with a fractional ordinary differential system. By the Lumer-Phillips theorem, we obtain the existence and uniqueness of the solution. Furthermore, we use a new Lyapunov functional to show the global attractivity for the considered system, then the tractable global attractive conditions are obtained. Finally, numerical examples are provided to illustrate the applications of our results.

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230039, China

    Mimi Hou, Xuan-Xuan Xi & Xian-Feng Zhou

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  1. Mimi Hou
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  2. Xuan-Xuan Xi
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  3. Xian-Feng Zhou
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Correspondence to Xian-Feng Zhou.

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This work was supported by National Natural Science Foundation of China (11471015 and 11601003); Natural Science Foundation of Anhui Province (1508085MA01, 1608085MA12, 1708085MA15 and 2008085QA19) and Program of Natural Science Research for Universities of Anhui Province (KJ2016A023).

Mimi Hou received her B.S. degree from Hefei Normal University in 2016, and her M.S. degree from Anhui University in 2019. She is currently working toward a Ph.D. degree at the School of Mathematical Sciences, Anhui University, Hefei, China. Her current research mainly concerns to stability, state feedback boundary control and event-triggered control of fractional coupled systems.

Xuan-Xuan Xi received his B.S. degree from Hefei Normal University in 2016, and his Ph.D. degree from Anhui University in 2021. His research interests include the well-posedness, regularity and stability of the solutions of fractional partial differential equations, as well as fractional control systems.

Xian-Feng Zhou received his M.S. degree from Anhui University in 2002, and his Ph.D. degree from University of Science and Technology of China in 2009, respectively. He is currently a professor at the School of Mathematical Sciences, Anhui University. His research interests include fractional partial functional differential systems and control systems. He is the author and co-author over 30 publications in journals.

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Hou, M., Xi, XX. & Zhou, XF. Asymptotic Behavior Analysis of a Heat Equation Coupled with a Fractional Ordinary Differential System. Int. J. Control Autom. Syst. 20, 3155–3166 (2022). https://doi.org/10.1007/s12555-020-0567-6

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  • DOI: https://doi.org/10.1007/s12555-020-0567-6

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