Stable spike clusters for the precursor Gierer-Meinhardt system in \(\mathbb {R}^2\)

DOI10.1007/s00526-017-1233-6zbMath1386.35166arXiv1705.08284OpenAlexW2758111367WikidataQ59522967 ScholiaQ59522967MaRDI QIDQ1674629

Wen Yang, Matthias Winter, Wei, Juncheng

Publication date: 25 October 2017

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.08284

zbMATH Keywords

Gierer-Meinhardt systemSpike cluster

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Developmental biology, pattern formation (92C15) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (12)

Stable boundary spike clusters for the two-dimensional Gierer-Meinhardt system ⋮ Turing–Hopf Bifurcation in Diffusive Gierer–Meinhardt Model ⋮ The effect of heterogeneity on one-peak stationary solutions to the Schnakenberg model ⋮ Existence and stability of symmetric and asymmetric patterns for the half-Laplacian Gierer–Meinhardt system in one-dimensional domain ⋮ Cluster solutions for the Fitzhugh-Nagumo system with Neumann boundary conditions ⋮ Spatial heterogeneity localizes Turing patterns in reaction-cross-diffusion systems ⋮ Multi-peak solutions for the Schnakenberg model with heterogeneity on star shaped graphs ⋮ Hexagonal spike clusters for some PDE's in 2D ⋮ Concentration phenomena on \(Y\)-shaped metric graph for the Gierer-Meinhardt model with heterogeneity ⋮ Multi-bump ground states of the fractional Gierer-Meinhardt system on the real line ⋮ Stable spike clusters on a compact two-dimensional Riemannian manifold ⋮ Pulse Solutions for an Extended Klausmeier Model with Spatially Varying Coefficients

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