Strongly coupled elliptic systems and applications to Lotka-Volterra models with cross-diffusion
type: Item
instance of: scholarly article
title: Strongly coupled elliptic systems and applications to Lotka-Volterra models with cross-diffusion
zbMATH Open document ID: 1074.35034
author: C. V. Pao
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-02-22T00:00:00Z
review text: The paper is concerned with the existence and method of construction of solutions for a general class of strongly coupled elliptic systems with three classical types of reaction functions that correspond to competition, prey-predator, and cooperating models. Application of the method of upper and lower solutions and associated monotone iterations lead to some positive solutions of the competition system and to quasisolutions of the predator-prey and cooperating systems. Sufficient conditions for the existence of a unique positive solution for each model are given.
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 2136802
zbMATH Keywords: elliptic systems
zbMATH Keywords: reaction-diffusion systems
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: monotone iterative method
zbMATH Keywords: positive solutions
zbMATH Keywords: quasisolutions
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
full work available at URL: j.na.2004.10.008
OpenAlex ID: W2067183512
cites work: A density-dependent diffusion system with stable discontinuous stationary solutions
cites work: Global existence for coupled reaction-diffusion systems
cites work: An initial-boundary-value problem for a certain density-dependent diffusion system
cites work: Smooth solutions to a quasi-linear system of diffusion equations for a certain population model
cites work: Diffusion, self-diffusion and cross-diffusion
cites work: On the global existence of a cross-diffusion system
cites work: Stationary pattern of some density-dependent diffusion system with competitive dynamics
cites work: Spatial segregation in competitive interaction-diffusion equations
cites work: Q3856484
cites work: Coexistence and stability of a competition-diffusion system in population dynamics
cites work: Numerical solutions for some coupled systems of nonlinear boundary value problems
cites work: Nonlinear elliptic boundary-value problems in unbounded domains
cites work: Quasisolutions and global attractor of reaction-diffusion systems
cites work: Numerical Analysis of Coupled Systems of Nonlinear Parabolic Equations
cites work: Global existence of solutions for a strongly coupled quasilinear parabolic system
cites work: Existence of the global attractor for a strongly coupled parabolic system arising in population dynamics
cites work: Positive steady-state solutions of a competing reaction-diffusion system with large cross-diffusion coefficients
cites work: Q4266656
cites work: Coexistence theorem of steady states for nonlinear self-cross diffusion systems with competitive dynamics.
cites work: Uniform boundedness and convergence of solutions to the systems with a single nonzero cross-diffusion
cites work: Uniform boundedness and convergence of solutions to the systems with cross-diffusions dominated by self-diffusions
cites work: Global solution to some quasilinear parabolic system in population dynamics
DOI: 10.1016/J.NA.2004.10.008
description: scientific article; zbMATH DE number 2136802