Stability of least energy patterns of the shadow system for an activator-inhibitor model.

DOI10.1007/BF03168574zbMath1200.35172OpenAlexW2018706150MaRDI QIDQ5944156

Wei-Ming Ni, Eiji Yanagida, Izumi Takagi

Publication date: 27 September 2001

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

Full work available at URL: https://doi.org/10.1007/bf03168574

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Developmental biology, pattern formation (92C15)

Related Items (31)

On positive solutions concentrating on spheres for the Gierer-Meinhardt system ⋮ Multidimensional boundary layers for a singularly perturbed Neumann problem ⋮ Hopf bifurcation from spike solutions for the weak coupling Gierer–Meinhardt system ⋮ An instability criterion for activator-inhibitor systems in a two-dimensional ball ⋮ An instability criterion for activator-inhibitor systems in a two-dimensional ball. II ⋮ Global existence and finite time blow-up of solutions of a Gierer-Meinhardt system ⋮ Concentration on minimal submanifolds for a singularly perturbed Neumann problem ⋮ Nonlocal eigenvalue problems arising in a generalized phase-field-type system ⋮ Multiple solutions to Gierer-Meinhardt systems ⋮ Concentration of solutions for a singularly perturbed Neumann problem in non-smooth domains ⋮ On large ring solutions for Gierer-Meinhardt system in \(\mathbb R^3\) ⋮ Singularly perturbed nonlinear Neumann problems with a general nonlinearity ⋮ Positive clustered layered solutions for the Gierer-Meinhardt system ⋮ Concentrating solutions of some singularly perturbed elliptic equations ⋮ A mathematical model of algae growth in a pelagic-benthic coupled shallow aquatic ecosystem ⋮ Existence, nonexistence and uniqueness of positive stationary solutions of a singular Gierer-Meinhardt system ⋮ ON THE GIERER–MEINHARDT SYSTEM WITH SATURATION ⋮ Global bifurcation and structure of Turing patterns in the 1-D Lengyel-Epstein model ⋮ The Gierer-Meinhardt system on a compact two-dimensional Riemannian manifold: Interaction of Gaussian curvature and Green's function ⋮ On the shape of the stable patterns for activator-inhibitor systems in two-dimensional domains ⋮ The spatially heterogeneous diffusive rabies model and its shadow system ⋮ Stable spike clusters on a compact two-dimensional Riemannian manifold ⋮ Stability Criteria for Reaction-Diffusion Systems with Skew-Gradient Structure ⋮ Stable and unstable periodic spiky solutions for the Gray-Scott system and the Schnakenberg system ⋮ Perturbative techniques for the construction of spike-layers ⋮ Concentration of Solutions for Some Singularly Perturbed Neumann Problems ⋮ Hopf bifurcation in a gene regulatory network model: Molecular movement causes oscillations ⋮ Positive steady states of an elliptic system arising from biomathematics ⋮ Patterns Versus Spatial Heterogeneity—From a Variational Viewpoint ⋮ Singularly perturbed nonlinear elliptic problems on manifolds ⋮ Multi-bump ground states of the Gierer-Meinhardt system in \(\mathbb R^2\).

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