异质介质中反应-扩散-ODE 系统的动力学特性

Pub Date : 2024-03-27 DOI:10.1007/s10255-024-1084-9

Cong-hui Zhang, Hai-feng Zhang, Mei-rong Zhang

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引用次数: 0

摘要

本文研究了反应-扩散-ODE 系统静止解的存在性和稳定性。我们首先证明了连续和非连续静止解的存在。然后，在适当的条件下，我们对非连续静止解的稳定性有了很好的理解。此外，我们还证明了扩散系数对静止解的影响。我们获得的结果是基于超/子求解法和广义山口定理。最后，我们给出了一些数值模拟来说明理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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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