Traveling wave solutions of a model of skin pattern formation in a singular case |
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Authors: | Bogdan Kaźmierczak Kazimierz Piechór |
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Institution: | Polish Academy of Sciences, IPPT PAN, ul. Pawińskiego 5B, PL 02‐106 Warszawa, Poland |
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Abstract: | 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. Copyright © 2010 John Wiley & Sons, Ltd. |
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Keywords: | skin morphogenesis heteroclinic solutions implicit function theorem |
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