Finite Travelling Waves for a Semilinear Degenerate Reaction-Diffusion System

In this paper, the existence and nonexistence of finite travelling waves (FTWs) for a semilinear degenerate reaction-diffusion system is studied, where 0 < α _i < 1, m _ij ≥ 0 and ∑ ^N _{j =1} m _ij > 0, i, j = 1,...,N. Necessary and sufficient conditions on existence and large time behaviours of FTWs of (I) are obtained by using the matrix theory, Schauder's fixed point theorem, and upper and lower solutions method. Received July 3, 1997, Revised June 23, 1999, Accepted March 29, 2000