Numerical approach to existence and stability of stationary solutions to a SKT cross-diffusion equation

DOI10.1142/S0218202518400122zbMath1411.35164OpenAlexW2805116390WikidataQ129733528 ScholiaQ129733528MaRDI QIDQ4630534

Takashi Suzuki, Tatsuki Mori, Shoji Yotsutani

Publication date: 27 March 2019

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202518400122

zbMATH Keywords

stabilityexact solutionSKT cross-diffusion equation

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) Population dynamics (general) (92D25) Ecology (92D40)

Related Items (8)

Global structure of steady-states to the full cross-diffusion limit in the Shigesada-Kawasaki-Teramoto model ⋮ Quasilinear reaction diffusion systems with mass dissipation ⋮ Hopf bifurcations in the full SKT model and where to find them ⋮ Coexistence-segregation dichotomy in the full cross-diffusion limit of the stationary SKT model ⋮ Cross-diffusion models: Analytic and multiscale problems ⋮ Full cross-diffusion limit in the stationary Shigesada-Kawasaki-Teramoto model ⋮ On the influence of cross-diffusion in pattern formation ⋮ On the limiting system in the Shigesada, Kawasaki and Teramoto model with large cross-diffusion rates

Cites Work

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• Stability of singularly perturbed solutions to nonlinear diffusion systems arising in population dynamics
• On a limiting system in the Lotka-Volterra competition with cross-diffusion.
• Diffusion, self-diffusion and cross-diffusion

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