Summary: DOI: 10.1007/s00332-003-0526-4
J. Nonlinear Sci. Vol. 13: pp. 449­470 (2003)
© 2003 Springer-Verlag New York Inc.
Existence of Travelling Wave Solutions in a Tissue
Interaction Model for Skin Pattern Formation
S. Ai
Department of Mathematical Sciences, University of Alabama in Huntsville,
Huntsville, AL 35899, USA
ais@email.uah.edu
Received June 6, 2002; accepted April 22, 2003
Online publication July 10, 2003
Communicated by P. K. Maini
Summary. We study a tissue interaction model on skin pattern formation proposed by
Cruywagen and Murray [J. Nonlin. Sci., 2 (1992), 217­240]. 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.
1991 Mathematics Subject Classification. 34C37, 92C37, 92C40
Key words. tissue interaction model, travelling wave solutions, singular perturbations

Source: Ai, Shangbing - Department of Mathematical Sciences, University of Alabama in Huntsville

Collections: Mathematics