Regular Article

Journal of Nonlinear Science

, Volume 13, Issue 5, pp 449-470

First online:

Existence of Travelling Wave Solutions in a Tissue Interaction Model for Skin Pattern Formation

  • S. AiAffiliated withDepartment of Mathematical Sciences, University of Alabama in Huntsville Email author 

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We study a tissue interaction model on skin pattern formation proposed by Cruywagen and Murray [J. Nonlin. Sci., 2 (1992), 217–240]. We prove rigorously that the model has travelling wave solutions for all sufficiently large wave speeds, which were found numerically by Cruywagen, Maini, and Murray [J. Math. Biol., 33 (1994), 193–210]. Our results also confirm the asymptotic expansions obtained for those solutions by formal perturbation analysis in the Cruywagen et al. article cited above.