Existence of standing waves for competition-diffusion equations

DOI10.1007/BF03167302zbMath0859.35054MaRDI QIDQ1922270

Yukio Kan-On

Publication date: 9 April 1997

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

zbMATH Keywords

comparison principleexponential dichotomytravelling waveLotka-Volterra typecompetition-diffusion equationpositive standing waves

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (31)

Instability of stationary solutions for a Lotka-Volterra competition model with diffusion ⋮ Asymptotic analysis of the bistable Lotka-Volterra competition-diffusion system ⋮ A note on the propagation speed of travelling waves for a Lotka-Volterra competition model with diffusion ⋮ Semi-exact equilibrium solutions for three-species competition-diffusion systems ⋮ Long time behavior of entire solutions to bistable reaction diffusion equations ⋮ Time periodic traveling curved fronts in the periodic Lotka-Volterra competition-diffusion system ⋮ Existence of front-back-pulse solutions of a three-species Lotka-Volterra competition-diffusion system ⋮ Lecture Notes on the Singular Limit of Reaction-diffusion Systems ⋮ Propagating direction in the two species Lotka-Volterra competition-diffusion system ⋮ Wave propagation for a two-component lattice dynamical system arising in strong competition models ⋮ Existence and stability of non-monotone travelling wave solutions for the diffusive Lotka–Volterra system of three competing species ⋮ Global bifurcation structure of positive stationary solutions for a classical Lotka-Volterra competition model with diffusion ⋮ Entire solutions of time periodic bistable Lotka-Volterra competition-diffusion systems in \(\mathbb{R}^N\) ⋮ Existence and instability of Neumann layer solutions for a 3-component Lotka-Volterra model with diffusion ⋮ Traveling waves for \(n\)-species competitive system with nonlocal dispersals and delays ⋮ Traveling wave solutions for two species competitive chemotaxis systems ⋮ Time periodic traveling fronts of pyramidal shapes for periodic Lotka-Volterra competition-diffusion system ⋮ On the existence of axisymmetric traveling fronts in Lotka-Volterra competition-diffusion systems in \(\mathbb{R}^3\) ⋮ Exact traveling wave solutions for diffusive Lotka-Volterra systems of two competing species ⋮ Entire solutions of diffusive Lotka-Volterra system ⋮ Traveling curved fronts of bistable Lotka-Volterra competition-diffusion systems in \(\mathbb{R}^3\) ⋮ The minimal speed of traveling fronts for the Lotka-Volterra competition system ⋮ Entire solutions for a two-component competition system in a lattice ⋮ Exact solutions of reaction-diffusion systems and nonlinear wave equations ⋮ Invasion entire solutions for two-species diffusive monostable competitive systems ⋮ Diffusive solutions of the competitive Lotka-Volterra system ⋮ The sign of traveling wave speed in bistable dynamics ⋮ Entire solutions originating from traveling fronts for a two-species competition-diffusion system ⋮ Traveling wave front for a two-component lattice dynamical system arising in competition models ⋮ Entire solutions for a delayed lattice competitive system ⋮ Stability analysis in order-preserving systems in the presence of symmetry

Cites Work

• Unnamed Item
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Existence of non-constant stable equilibria in competition-diffusion equations
• Instability of stationary solutions for a Lotka-Volterra competition model with diffusion
• A 3-component system of competition and diffusion
• Stability of monotone travelling waves for competition-diffusion equations
• Homoclinic and heteroclinic bifurcations of Vector fields
• Stability of equilibrium solutions for the Fisher equation
• Parameter Dependence of Propagation Speed of Travelling Waves for Competition-Diffusion Equations

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