Spikes for the Gierer-Meinhardt system with discontinuous diffusion coefficients

DOI10.1007/s00332-008-9036-8zbMath1183.35021OpenAlexW2101152357MaRDI QIDQ733763

Matthias Winter, Wei, Juncheng

Publication date: 19 October 2009

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00332-008-9036-8

zbMATH Keywords

stabilityNeumann boundary conditionsLyapunov-Schmidt methoddiscontinuous diffusion coefficientnonlocal eigenvalue problemspiky patterns

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Biochemistry, molecular biology (92C40) Developmental biology, pattern formation (92C15) Initial-boundary value problems for second-order parabolic systems (35K51) Pattern formations in context of PDEs (35B36)

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Cites Work

• Unnamed Item
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• On the Gierer-Meinhardt system with precursors
• Diffusion driven instability in an inhomogeneous domain
• Unravelling the Turing bifurcation using spatially varying diffusion coefficients
• Analysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients
• Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model
• Spikes for the two-dimensional Gierer-Meinhardt system: the weak coupling case
• Spikes for the Gierer-Meinhardt system in two dimensions: the strong coupling case
• Complex pattern formation in reaction-diffusion systems with spatially varying parameters
• Pattern formation in spatially heterogeneous Turing reaction-diffusion models
• On stability and Hopf bifurcations for chemotaxis systems
• The Dynamics and Pinning of a Spike for a Reaction-Diffusion System
• Dynamics of traveling pulses in heterogeneous media
• Binary fluid convection in a rotating cylinder
• The chemical basis of morphogenesis
• On the Two-Dimensional Gierer--Meinhardt System with Strong Coupling
• On single interior spike solutions of the Gierer–Meinhardt system: uniqueness and spectrum estimates
• The stability of spike solutions to the one-dimensional Gierer-Meinhardt model