Reaction-diffusion systems in the Gierer-Meinhardt theory of biological pattern formation

DOI10.1007/BF03167754zbMath0656.92004WikidataQ113906548 ScholiaQ113906548MaRDI QIDQ3804495

Kyuya Masuda, Katsuo Takahashi

Publication date: 1987

Published in: Japan Journal of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

existence of positive solutionspattern formationinitial conditionsequilibrium solutionsno-flux boundary conditionsGierer-Meinhardt systemsformation of spatial patterns of tissue structurenonexistence of patterns

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Reaction-diffusion equations (35K57) General biology and biomathematics (92B05)

Related Items (18)

The stochastic Gierer-Meinhardt system ⋮ Analysis and asymptotic reduction of a bulk-surface reaction-diffusion model of Gierer-Meinhardt type ⋮ Upper semicontinuity of the global attractor for the Gierer-Meinhardt model ⋮ On the global existence and finite time blow-up of shadow systems ⋮ Finite-time blowup of solutions to some activator-inhibitor systems ⋮ The dynamics of a kinetic activator -- inhibitor system ⋮ Global existence and finite time blow-up of solutions of a Gierer-Meinhardt system ⋮ Some results on the Gierer-Meinhardt model with critical exponent \(p - 1 = r\) ⋮ A remark on global existence of solutions of shadow systems ⋮ On global existence for the Gierer-Meinhardt system ⋮ Global existence and blowup solutions for the Gierer-Meinhardt system ⋮ Dynamical system for animal coat pattern model ⋮ Dynamics of shadow system of a singular Gierer-Meinhardt system on an evolving domain ⋮ Large-time behaviour and blow up of solutions for Gierer-Meinhardt systems ⋮ The spatially heterogeneous diffusive rabies model and its shadow system ⋮ Global solutions for an \(m\)-component system of activator-inhibitor type ⋮ GLOBAL ANALYSIS OF THE SHADOW GIERER-MEINHARDT SYSTEM WITH GENERAL LINEAR BOUNDARY CONDITIONS IN A RANDOM ENVIRONMENT ⋮ Remarks on pattern formation in a model for hair follicle spacing

Cites Work

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• On the global existence and asymptotic behavior of solutions of reaction- diffusion equations
• Point-condensation for a reaction-diffusion system
• A priori estimates for stationary solutions of an activator-inhibitor model due to Gierer and Meinhardt
• A bifurcation analysis of pattern formation in a diffusion governed morphogenetic field
• On the Neumann Problem for Some Semilinear Elliptic Equations and Systems of Activator-Inhibitor Type

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