V. Hutson et K. Mischaikow, SINGULAR LIMITS FOR TRAVELING WAVES FOR A PAIR OF EQUATIONS, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 126, 1996, pp. 399-411
The singular limit as one diffusion coefficient approaches zero is con
sidered for travelling wave solutions to a pair of reaction-diffusion
equations. An explicit criterion determining the sign of the wave spee
d is obtained. The limit behaviour turns out to be of a different natu
re for positive and negative wave speed. Different techniques, which m
ay be applicable to a range of examples, are needed in the two cases.