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Traveling wave solutions of a model of skin pattern formation in a singular case

✍ Scribed by Bogdan Kaźmierczak; Kazimierz Piechór

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
201 KB
Volume
34
Category
Article
ISSN
0170-4214

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✦ Synopsis

Communicated by J. Banasiak

We study traveling wave solutions to a system of four non-linear partial differential equations, which arise in a tissue interaction model for skin morphogenesis. Under the assumption that the strength of attachment of the epidermis to the basal lamina is sufficiently large, we prove the existence and uniqueness (up to a translation) of traveling wave solutions connecting two stationary states of the system with the dermis and epidermis cell densities being positive. We discuss the problem of the minimal wave speed.

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