Spike‐Type Solutions to One Dimensional Gierer–Meinhardt Model with Lévy Flights

DOI10.1111/j.1467-9590.2012.00550.xzbMath1263.35145OpenAlexW1570844200MaRDI QIDQ4906047

Yana Nec

Publication date: 21 February 2013

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/j.1467-9590.2012.00550.x

zbMATH Keywords

fractional differential equationLévy flightsalgebraically decaying tails

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57)

Related Items

Stability of Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain ⋮ Turing-Hopf bifurcation analysis in a superdiffusive predator-prey model ⋮ Dynamics of pulse solutions in Gierer-Meinhardt model with time dependent diffusivity ⋮ Existence and stability of symmetric and asymmetric patterns for the half-Laplacian Gierer–Meinhardt system in one-dimensional domain ⋮ Turing Patterns in the Lengyel–Epstein System with Superdiffusion ⋮ Multi-spike solutions to the one-dimensional subcritical fractional Schnakenberg system ⋮ Spike solutions to the supercritical fractional Gierer-Meinhardt system ⋮ Multi-bump ground states of the fractional Gierer-Meinhardt system on the real line ⋮ Pattern formation by super-diffusion in Fitzhugh-Nagumo model ⋮ On accuracy of numerical solution to boundary value problems on infinite domains with slow decay

Cites Work

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• On the Evaluation of Certain Sums Involving the Natural Numbers Raised to an Arbitrary Power
• The stability of spike solutions to the one-dimensional Gierer-Meinhardt model
• The random walk's guide to anomalous diffusion: A fractional dynamics approach