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