Abstract
In this paper, we consider the Gierer–Meinhardt model with the heterogeneity in both the activator and the inhibitor on the Y-shaped compact metric graph. Using the Lyapunov–Schmidt reduction method, we construct a one-peak stationary solution, which concentrates at a suitable point. In particular, we reveal that the location of concentration point is determined by the interaction of the heterogeneity function for the activator with the geometry of the domain, represented by the associated Green’s function. Moreover, based on our main result, we determine the precise location of concentration point for non-heterogeneity case. Furthermore, we also present the effect of heterogeneity by using a concrete example.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
