Regular and Discontinuous Solutions in a Reaction-Diffusion Model for Hair Follicle Spacing
Keywords:dynamical systems, reaction-diffusion equations, stationary solutions, weak solutions
AbstractSolutions of a model reaction-diffusion system inspired by a model for hair follicle initiation in mice are constructed and analysed for the case of a one-dimensional domain. It is shown that all regular spatially heterogeneous solutions of the problem are unstable. Numerical tests show that the only asymptotically stable weak solutions are those with large jump discontinuities.
The journal Biomath is an open access journal. All published articles are immeditely available online and the respective DOI link activated. All articles can be access for free and no reader registration of any sort is required. No fees are charged to authors for article submission or processing. Online publications are funded through volunteer work, donations and grants.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).