A reaction-diffusion system of a competitor-competitor-mutualist model
type: Item
instance of: scholarly article
title: A reaction-diffusion system of a competitor-competitor-mutualist model
zbMATH Open document ID: 0658.35053
DOI: 10.1016/0022-247X(87)90038-2
author: Sining Zheng
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: We investigate the homogeneous Dirichlet problem and Neumann problem to a reaction-diffusion system of a competitor-competitor-mutualist model. The existence, uniqueness, and boundedness of the solutions are established by means of the comparison principle and the monotonicity method. For the Dirichlet problem, we study the existence of trivial and nontrivial nonnegative equilibrium solutions and their stabilities. For the Neumann problem, we analyze the constant equilibrium solutions and their stabilities. The main method used in studying of the stabilities is the spectral analysis to the linearized operators. The O.D.E. problem to the same model was proposed and studied by \textit{B. Rai}, \textit{H. I. Freedman}, and \textit{J. F. Addicott} [Math. Biosci. 65, 13-50 (1983; Zbl 0532.92025)].
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 4075652
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Neumann problem
zbMATH Keywords: reaction-diffusion system
zbMATH Keywords: competitor-competitor-mutualist model
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: boundedness
zbMATH Keywords: comparison principle
zbMATH Keywords: monotonicity
zbMATH Keywords: equilibrium
Wikidata QID: Q111266093
MaRDI profile type: Publication
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full work available at URL: 0022-247x(87)90038-2
OpenAlex ID: W2062570668
description: scientific article; zbMATH DE number 4075652