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Existence of Travelling Wave Solutions in a Tissue Interaction Model for Skin Pattern Formation
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Regular ArticleExistence of Travelling Wave Solutions
in a Tissue Interaction Model
for Skin Pattern Formation S. Ai1  | (1) | Department of Mathematical Sciences, University
of Alabama in Huntsville, Huntsville, AL 35899, USA |
Received: 6 June 2002 Accepted: 22 April 2003 Published online: 17 July 2003 Communicated by P.K. Maini 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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