Dynamics of metastable localized patterns and its application to the interaction of spike solutions for the Gierer-Meinhardt systems in two spatial dimensions
type: Item
instance of: scholarly article
title: Dynamics of metastable localized patterns and its application to the interaction of spike solutions for the Gierer-Meinhardt systems in two spatial dimensions
zbMATH Open document ID: 1029.35130
DOI: 10.1007/BF03167453
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 2004-01-29T00:00:00Z
review text: The authors investigate the so-called Gierer-Meinhardt system describing pattern formation in the regeneration of hydra amenable. They prove the existence and stability of a single spike solution. They also investigate the interaction of multi-spike solutions in two spatial dimensions when the distances between them are sufficiently large. It explains and clarifies a part of mechanism of the evolution process of localized patterns observed in simulations of the Gierer-Meinhardt model.
reviewed by: Daniel Ševčovič
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35Q80
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35-02
zbMATH DE Number: 1802940
zbMATH Keywords: interaction of spike solutions
zbMATH Keywords: Gierer-Meinhardt model
zbMATH Keywords: reaction-diffusion system
zbMATH Keywords: Turing instability
zbMATH Keywords: pattern formation
Wikidata QID: Q121689719
author: Shin-Ichiro Ei
author: Juncheng Wei
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1802940