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Stability and asymptotic behaviour in a reaction–diffusion system
Author(s) -
Feng Wei
Publication year - 1994
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670170302
Subject(s) - mathematics , neumann boundary condition , reaction–diffusion system , exponential stability , robin boundary condition , dirichlet boundary condition , mathematical analysis , constant (computer programming) , stability (learning theory) , boundary value problem , steady state (chemistry) , component (thermodynamics) , dirichlet distribution , homogeneous , diffusion , boundary (topology) , nonlinear system , thermodynamics , chemistry , physics , quantum mechanics , machine learning , combinatorics , computer science , programming language
This paper is concerned with some qualitative analysis for a coupled system of five reaction–diffusion equations which arises from a physiology model. The uniform boundedness of the time‐dependent solution is obtained under various boundary conditions. Sufficient conditions are also given to ensure the asymptotic stability of the non‐negative steady‐state solutions under Dirichlet or Robin boundary condition for each component. Under homogeneous Neumann boundary condition for some components the time‐dependent solution is proven to converge to a constant steady state determined by the initial functions.