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

Existence of Travelling Wave Solutions in a Tissue Interaction Model for Skin Pattern Formation S. Ai ais@email.uah.edu Department of Mathematical Sciences, University of Alabama in Huntsville Huntsville, AL 35899 USA 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Nonlinear Science Springer Journals

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