The stability of nontrivial positive steady states for the SKT model with large cross diffusion

DOI10.1007/s10255-020-0951-2zbMath1462.35056OpenAlexW3082647335MaRDI QIDQ2023738

Qing Li, Qian Xu

Publication date: 3 May 2021

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10255-020-0951-2

zbMATH Keywords

stability of steady statesspectral analysiscross-diffusion systemnontrivial positive steady states

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Bifurcations in context of PDEs (35B32) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items

Global structure of steady-states to the full cross-diffusion limit in the Shigesada-Kawasaki-Teramoto model ⋮ Coexistence-segregation dichotomy in the full cross-diffusion limit of the stationary SKT model ⋮ On a limiting system of the triangular SKT competition model with large cross-diffusion and random-diffusion

Cites Work

• The existence and stability of nontrivial steady states for S-K-T competition model with cross diffusion
• Pattern formation in a cross-diffusion system
• The existence and structure of large spiky steady states for S-K-T competition systems with cross-diffusion
• On limit systems for some population models with cross-diffusion
• The existence and stability of traveling waves with transition layers for the S-K-T competition model with cross-diffusion
• Coexistence problem for two competing species models with density- dependent diffusion
• Geometric theory of semilinear parabolic equations
• Diffusion vs cross-diffusion: An elliptic approach
• Stability of singularly perturbed solutions to nonlinear diffusion systems arising in population dynamics
• Bifurcation theory. An introduction with applications of PDEs
• Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion
• On a limiting system in the Lotka-Volterra competition with cross-diffusion.
• On the global existence of a cross-diffusion system
• Stability analysis on a type of steady state for the SKT competition model with large cross diffusion
• Diffusion, self-diffusion and cross-diffusion
• Positive steady-state solutions of a competing reaction-diffusion system with large cross-diffusion coefficients
• Bifurcation, perturbation of simple eigenvalues, and linearized stability
• Instability of spiky steady states for S-K-T biological competing model with cross-diffusion
• The instability of spiky steady states for a competing species model with cross diffusion
• Limiting Structure of Shrinking Solutions to the Stationary Shigesada--Kawasaki--Teramoto Model with Large Cross-Diffusion
• Positive solutions for Lotka–Volterra competition systems with large cross-diffusion
• Cross Diffusion Systems on 2 Spatial Dimensional Domains
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item