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Remarks on pattern formation in a model for hair follicle spacing. (English) Zbl 1334.35133

Summary: A modified version of the Gierer-Meinhardt reaction-diffusion system (without source terms) is used in a model for hair follicle spacing in mice, proposed by S. Sick et al. [“WNT and DKK determine hair follicle spacing through a reaction-diffusion mechanism”, Science 314, No. 5804, 1447–1450 (2006; doi:10.1126/science.1130088)]. Global existence of solutions of this model system is shown by computing uniform bounds. Analysis of conditions for emergence of spatially heterogeneous solutions is performed using a limiting form of the original reaction-diffusion system. The conditions for pattern formation given in [loc. cit.] are improved by including those subregions in the parameter space where far-from-equilibrium heterogeneous solutions occur.

MSC:

35K57 Reaction-diffusion equations
35B36 Pattern formations in context of PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences

Software:

FreeFem++
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Full Text: DOI

References:

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