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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.



Journal of Nonlinear ScienceSpringer Journals

Published: Oct 1, 2003

DOI: 10.1007/s00332-003-0526-4

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