The Gierer-Meinhardt system on a compact two-dimensional Riemannian manifold: Interaction of Gaussian curvature and Green's function

DOI10.1016/J.MATPUR.2010.03.003zbMath1204.58026OpenAlexW2033046904WikidataQ115343589 ScholiaQ115343589MaRDI QIDQ710545

Wang Hung Tse, Matthias Winter, Wei, Juncheng

Publication date: 19 October 2010

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2010.03.003

zbMATH Keywords

singular perturbationGreen's functionRiemannian manifoldpattern formationGaussian curvaturemathematical biologyspiky solutionsGierer-Meinhardt systemmodel morphogenesis

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20) General biology and biomathematics (92B05)

Related Items (8)

Influence of curvature, growth, and anisotropy on the evolution of Turing patterns on growing manifolds ⋮ Multi-spike solutions to the one-dimensional subcritical fractional Schnakenberg system ⋮ Spike solutions to the supercritical fractional Gierer-Meinhardt system ⋮ Stable spike clusters on a compact two-dimensional Riemannian manifold ⋮ Spot patterns of the Schnakenberg reaction–diffusion system on a curved torus ⋮ Analysis of Spot Patterns on a Coordinate-Invariant Model for Vegetation on a Curved Terrain ⋮ Diffusive instabilities and spatial patterning from the coupling of reaction–diffusion processes with Stokes flow in complex domains ⋮ The Stability of Localized Spot Patterns for the Brusselator on the Sphere

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