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Some heteroclinic solutions of a model of skin pattern formation
Author(s) -
Kaźmierczak Bogdan,
Piechór Kazimierz
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.511
Subject(s) - uniqueness , mathematics , perturbation (astronomy) , traveling wave , epidermis (zoology) , morphogenesis , partial differential equation , mathematical analysis , dermis , translation (biology) , pattern formation , anatomy , physics , chemistry , biology , biochemistry , quantum mechanics , messenger rna , gene , genetics
In this paper we study travelling wave solutions to a system of four non‐linear partial differential equations, which arise in a tissue interaction model for skin morphogenesis. Under the ‘small‐stress’ assumption we prove the existence and uniqueness (up to a translation) of solutions with the dermis and epidermis cell densities being positive, which are a perturbation of a uniform epidermal cell density. We discuss the problem of the minimal wave‐speed. Copyright © 2004 John Wiley & Sons, Ltd.