An Asymptotic Analysis of Localized Three-Dimensional Spot Patterns for the Gierer--Meinhardt Model: Existence, Linear Stability, and Slow Dynamics

DOI10.1137/20M135707XzbMath1462.35031arXiv2008.04535MaRDI QIDQ4986535

Wei, Juncheng, Michael J. Ward, Daniel Gómez

Publication date: 27 April 2021

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.04535

zbMATH Keywords

matched asymptotic expansionssmall activator diffusivitylocalized spot patterns

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Asymptotic expansions of solutions to PDEs (35C20) Pattern formations in context of PDEs (35B36)

Related Items

Stability of Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain, Oscillatory translational instabilities of spot patterns in the Schnakenberg system on general 2D domains, Multi-spike solutions to the one-dimensional subcritical fractional Schnakenberg system, Spike solutions to the supercritical fractional Gierer-Meinhardt system, Boundary layer solutions in the Gierer-Meinhardt system with inhomogeneous boundary conditions

Uses Software

• FlexPDE

Cites Work

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