Journal of Nonlinear Science

, Volume 13, Issue 5, pp 449–470

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

Regular Article

DOI: 10.1007/s00332-003-0526-4

Cite this article as:
Ai, S. J. Nonlinear Sci. (2003) 13: 449. doi:10.1007/s00332-003-0526-4

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.

Copyright information

© Springer-Verlag New York Inc. 2003

Authors and Affiliations

  1. 1.Department of Mathematical Sciences, University of Alabama in HuntsvilleUSA