Construction of multi-peak solutions to the Gierer-Meinhardt system with saturation and source term

DOI10.1016/j.na.2009.01.089zbMath1178.35040OpenAlexW1979960475MaRDI QIDQ923908

Kotaro Morimoto

Publication date: 24 July 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.01.089

zbMATH Keywords

homogeneous Neumann boundary conditionnonlinear elliptic systemsaturation effect

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Nonlinear elliptic equations (35J60) Developmental biology, pattern formation (92C15) Boundary value problems for second-order elliptic systems (35J57) Pattern formations in context of PDEs (35B36)

Related Items (4)

An explicit theory for pulses in two component, singularly perturbed, reaction-diffusion equations ⋮ On positive solutions generated by semi-strong saturation effect for the Gierer-Meinhardt system ⋮ Bifurcation analysis of the Gierer–Meinhardt system with a saturation in the activator production ⋮ Point-condensation phenomena and saturation effect for the one-dimensional Gierer-Meinhardt system

Cites Work

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• Construction and asymptotic behavior of multi-peak solutions to the Gierer-Meinhardt system with saturation
• On Multiple Mixed Interior and Boundary Peak Solutions for Some Singularly Perturbed Neumann Problems
• ON THE GIERER–MEINHARDT SYSTEM WITH SATURATION
• On the Two-Dimensional Gierer--Meinhardt System with Strong Coupling
• The stability of spike solutions to the one-dimensional Gierer-Meinhardt model

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