Coexistence-equilibria for competition-diffusion systems with a small diffusion rate

DOI10.1007/BF03167062zbMath0635.35048OpenAlexW2057966133MaRDI QIDQ3774241

Masayuki Ito

Publication date: 1984

Published in: Japan Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03167062

zbMATH Keywords

singular perturbationhomogeneous Dirichlet boundary conditionscoexistencecompetition-diffusion systemtwo competing speciescoexistence stationary solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Singular perturbations in context of PDEs (35B25) Initial-boundary value problems for second-order parabolic equations (35K20) Population dynamics (general) (92D25) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (2)

Short note on a solution with large amplitude for the limiting system arising from the competition-diffusion system ⋮ Coexistence-segregation dichotomy in the full cross-diffusion limit of the stationary SKT model

Cites Work

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• Reaction-diffusion equations for competing species singularly perturbed by a small diffusion rate
• On stable space dependent stationary solutions of a competition system with diffusion
• Global aspect of steady-states for competitive-diffusive systems with homogeneous Dirichlet conditions
• Phase-plane solutions to some singular perturbation problems
• Boundary and interior transition layer phenomena for pairs of second- order differential equations
• Stability and bifurcation of steady-state solutions for predator-prey equations
• Non-degenerate solutions of boundary-value problems

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