A priori estimates for stationary solutions of an activator-inhibitor model due to Gierer and Meinhardt

DOI10.2748/tmj/1178229312zbMath0493.35004OpenAlexW2028475598MaRDI QIDQ1168489

Izumi Takagi

Publication date: 1982

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178229312

zbMATH Keywords

reaction-diffusion systemstationary solutionshomogeneous Neumann boundary conditionbiological pattern formationglobal behavior of solution branchessmoothly bounded domain

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) A priori estimates in context of PDEs (35B45) Perturbations in context of PDEs (35B20) Physiological, cellular and medical topics (92Cxx)

Related Items (5)

Point-condensation for a reaction-diffusion system ⋮ Global existence and finite time blow-up of solutions of a Gierer-Meinhardt system ⋮ Reaction-diffusion systems in the Gierer-Meinhardt theory of biological pattern formation ⋮ On the Neumann Problem for Some Semilinear Elliptic Equations and Systems of Activator-Inhibitor Type ⋮ Remarks on pattern formation in a model for hair follicle spacing

Cites Work

• Unnamed Item
• Unnamed Item
• Stability of bifurcating solutions of the Gierer-Meinhardt system
• Analytical treatment of pattern formation in the Gierer-Meinhardt model of morphogenesis
• Some global results for nonlinear eigenvalue problems
• Bifurcation from simple eigenvalues
• Stationary solutions of reaction-diffusion equations
• Bifurcation theory for Fredholm operators
• Activators and Inhibitors in Pattern Formation

This page was built for publication: A priori estimates for stationary solutions of an activator-inhibitor model due to Gierer and Meinhardt