Spiky patterns for the Schnakenberg model with advection term on Y-shaped metric graph

In this paper, we study the existence of spiky stationary solutions for reaction-diffusion-advection systems on the Y-shaped metric graph. Considering the Schnakenberg chemical reaction system with advection term, we investigate the effect of the advection and the network-structure of the graph on s...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 535; no. 2; p. 128149
Main Author Ishii, Yuta
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.07.2024
Subjects
Advection
Metric graph
Pattern formation
Schnakenberg model
Singular perturbation
Spike solution
Spike solution
Pattern formation
Schnakenberg model
Advection
Metric graph
Singular perturbation
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Summary:In this paper, we study the existence of spiky stationary solutions for reaction-diffusion-advection systems on the Y-shaped metric graph. Considering the Schnakenberg chemical reaction system with advection term, we investigate the effect of the advection and the network-structure of the graph on spiky solutions in details. In particular, the location and amplitude of spikes are decided by the interaction of the advection with the geometry of the graph, represented by the associated Green's functions. Moreover, we show that the direction of the shift of spikes depends on the choice of boundary conditions and the size of the advection velocity.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2024.128149