Stability of Spiky Solutions in a Competition Model with Cross-Diffusion

DOI10.1137/100808381zbMath1259.35018OpenAlexW2080755434MaRDI QIDQ3097540

Wei, Juncheng, Theodore Kolokolnikov

Publication date: 10 November 2011

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/34457fc68a3fb61b4263ae48d67accf8f3c2bb64

zbMATH Keywords

stabilitysingular perturbationpattern formationreaction-diffusion systemscross-diffusionformal asymptoticsShigesada-Kawasaki-Teramoto modelspike solutions

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Semilinear parabolic equations (35K58) Initial-boundary value problems for second-order parabolic systems (35K51) Pattern formations in context of PDEs (35B36)

Related Items (13)

Global structure of steady-states to the full cross-diffusion limit in the Shigesada-Kawasaki-Teramoto model ⋮ Limiting Structure of Shrinking Solutions to the Stationary Shigesada--Kawasaki--Teramoto Model with Large Cross-Diffusion ⋮ Coexistence-segregation dichotomy in the full cross-diffusion limit of the stationary SKT model ⋮ Qualitative analysis of a Lotka-Volterra competition system with advection ⋮ The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime ⋮ Full cross-diffusion limit in the stationary Shigesada-Kawasaki-Teramoto model ⋮ Global well-posedness, pattern formation and spiky stationary solutions in a Beddington-DeAngelis competition system ⋮ Limiting structure of steady-states to the Lotka-Volterra competition model with large diffusion and advection ⋮ Asynchronous Instabilities of Crime Hotspots for a 1-D Reaction-Diffusion Model of Urban Crime with Focused Police Patrol ⋮ Steady states of Lotka-Volterra competition models with nonlinear cross-diffusion ⋮ Global well-posedness of advective Lotka–Volterra competition systems with nonlinear diffusion ⋮ Dynamical analysis of a plateau pika with cross-diffusion under contraception control ⋮ Stability and dynamics of spike-type solutions to delayed Gierer-Meinhardt equations

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