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Dynamics of a Reaction-diffusion-ODE System in a Heterogeneous Media

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Abstract

The existence and stability of stationary solutions for a reaction-diffusion-ODE system are investigated in this paper. We first show that there exist both continuous and discontinuous stationary solutions. Then a good understanding of the stability of discontinuous stationary solutions is gained under an appropriate condition. In addition, we demonstrate the influences of the diffusion coefficient on stationary solutions. The results we obtained are based on the super-/sub-solution method and the generalized mountain pass theorem. Finally, some numerical simulations are given to illustrate the theoretical results.

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Acknowledgments

The authors would like to express their sincere gratitude to the anonymous referees for their critical reading of the manuscript. C.H. Zhang would like to thank Prof. Izumi Takagi for his help and encouragement.

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Authors and Affiliations

  1. School of Science, Beijing University of Civil Engineering and Architecture, Beijing, 102616, China

    Cong-hui Zhang

  2. Institute of Applied System Analysis, Jiangsu University, Zhenjiang, 212013, China

    Hai-feng Zhang

  3. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Mei-rong Zhang

Authors
  1. Cong-hui Zhang
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  2. Hai-feng Zhang
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  3. Mei-rong Zhang
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Corresponding author

Correspondence to Hai-feng Zhang.

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Mei-rong ZHANG is an editor of for Acta Mathematicae Applicatate Sinica (English Series) and was not involved in the editorial review or the decision to publish this article. All authors declare that there are no competing interests.

Additional information

The project is supported by National Natural Science Foundation of China (Grant No. 11790273, 52276028).

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Zhang, Ch., Zhang, Hf. & Zhang, Mr. Dynamics of a Reaction-diffusion-ODE System in a Heterogeneous Media. Acta Math. Appl. Sin. Engl. Ser. 40, 275–301 (2024). https://doi.org/10.1007/s10255-024-1084-9

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  • DOI: https://doi.org/10.1007/s10255-024-1084-9

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