Remarks on pattern formation in a model for hair follicle spacing

Peter Rashkov

doi:10.3934/dcdsb.2015.20.1555

Article Contents

2015, Volume 20, Issue 5: 1555-1572. Doi: 10.3934/dcdsb.2015.20.1555

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Remarks on pattern formation in a model for hair follicle spacing

Peter Rashkov^1,

1.
Department of Mathematics and Informatics, Philipps-Universitat Marburg, Hans-Meerwein-Str., Lahnberge, 35032 Marburg

Received: May 31, 2014

Revised: December 31, 2014

Published: June 2015

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Abstract

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 Sick, Reinker, Timmer and Schlake [22]. 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 [22] are improved by including those subregions in the parameter space where far-from-equilibrium heterogeneous solutions occur.

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Mathematics Subject Classification: Primary: 35K57, 35B36; Secondary: 35Q92.

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