Finite travelling waves for a semilinear degenerate reaction-diffusion system

In this paper, the existence and nonexistence of finite travelling waves (F TWs) for a semilinear degenerate reaction-diffusion system (u(i),(alphai))(t) = u(ixx) - Pi (N)(j=1) u(j)(mij), x is an element of R, t > 0, i = 1,...,N (I) is studied, where 0 < alpha (i) < 1, m(ij) greater than or equal to 0 and S igma (N)(j=1) m(ij) > 0, i, j = 1,...,N. Necessary and sufficient condition s on existence and large time behaviours. of FTWs of (I) are obtained by us ing the matrix theory, Schauder's fixed point theorem, and upper and lower solutions method.