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

作　　者：Cong-hui ZHANG Hai-feng ZHANG Mei-rong ZHANG 

机构地区：[1]School of Science,Beijing University of Civil Engineering and Architecture,Beijing 102616,China [2]Institute of Applied System Analysis,Jiangsu University,Zhenjiang 212013,China [3]Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第2期275-301,共27页应用数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11790273,52276028).

摘　　要：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.

关 键 词：reaction-diffusion-ODE system discontinuous stationary solutions stability asymptotic behavior monotone solutions 

分 类 号：O175[理学—数学]