Turing instability conditions for growing domains with divergence free mesh velocity

DOI10.1016/j.na.2009.05.027zbMath1239.35167OpenAlexW1964675167MaRDI QIDQ425804

Anotida Madzvamuse

Publication date: 9 June 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.05.027

zbMATH Keywords

pattern formationTuring instabilitygrowing domainsSchnakenberg modeldiffusion-driven instabilitynon-autonomous system of partial differential equations

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Traveling wave solutions (35C07)

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Pattern formation on a growing oblate spheroid. An application to adult sea urchin development ⋮ Stability analysis of reaction-diffusion models on evolving domains: the effects of cross-diffusion ⋮ Stability on time-dependent domains: convective and dilution effects ⋮ Spontaneous infection and periodic evolving of domain in a diffusive SIS epidemic model ⋮ The surface finite element method for pattern formation on evolving biological surfaces ⋮ Numerical study of three-dimensional Turing patterns using a meshless method based on moving Kriging element free Galerkin (EFG) approach ⋮ Computational examples of reaction-convection-diffusion equations solution under the influence of fluid flow: first example ⋮ Turing pattern formation on periodic geometrical figures with continuous growing: numerical experiments ⋮ Problems on time-varying domains: formulation, dynamics, and challenges

Cites Work

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• A numerical approach to the study of spatial pattern formation in the ligaments of arcoid bivalves
• Stability analysis of non-autonomous reaction-diffusion systems: The effects of growing domains
• Reaction and diffusion on growing domains: scenarios for robust pattern formation
• Velocity-induced numerical solutions of reaction-diffusion systems on continuously growing domains
• Stability analysis of reaction-diffusion systems with constant coefficients on growing domains
• Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth
• A moving grid finite element method applied to a model biological pattern generator
• The effect of growth and curvature on pattern formation
• Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains
• A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains
• The chemical basis of morphogenesis
• Phase differences in reaction-diffusion-advection systems and applications to morphogenesis

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