Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (4): 1171-1183.

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Globally Asymptotic Stability of 2-Species Reaction-Diffusion Systems of Spatially Inhomogeneous Models

Lv Dongting()   

  1. chool of Mathematical Sciences, Peking University, Beijing 100871
  • Received:2024-09-07 Revised:2025-02-11 Online:2025-08-26 Published:2025-08-01

Abstract:

The paper discusses the Neumann problem for 2-species reaction-diffusion system of spatially inhomogeneous models. When the reaction function of the species is non-monotonic with respect to its population density, firstly the existence of a unique positive equilibrium solution for both species is established by virtue of the sub-super solution technique. It is also proven that the positive equilibrium solution is globally asymptotically stable when the diffusion coefficients are sufficiently small. Finally, the correctness of the conclusion is verified through numerical solutions of a specific example.

Key words: spatially inhomogeneous model, globally asymptotic stability, positive equilibrium solution, reaction-diffusion system

CLC Number: 

  • O175.21
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