Abstract
It is known that for special types of reaction–diffusion Systems, such as the Gierer–Meinhardt model and the Gray-Scott model, stable stationary spike solutions exist on boundary points with maximal curvature. In this paper, we rigorously give the equation describing the motion of spike solutions along boundaries for general types of reaction–diffusion systems in R 2. We also apply the general results to the Gierer–Meinhardt model and show that a single spike solution moves toward a boundary point with locally maximal curvature. Moreover, by showing the repulsive interaction of spikes along boundaries for solutions of the Gierer–Meinhardt model, we have stable multispike stationary solutions in the neighborhood of a boundary point with locally maximal curvature.
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This paper is supported by a Grant-in-Aid for Scientific Research (No. 21654019).
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Ei, SI., Ishimoto, T. Dynamics and interactions of spikes on smoothly curved boundaries for reaction–diffusion systems in 2D. Japan J. Indust. Appl. Math. 30, 69–90 (2013). https://doi.org/10.1007/s13160-012-0088-7
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DOI: https://doi.org/10.1007/s13160-012-0088-7