On the wave front solution of a competition–diffusion system in population dynamics

In this paper, we consider a competition–diffusion system of two equations [Zhou and Pao, Asymptotic behavior of a competition–diffusion system in population dynamics, Nonlinear Anal. 6 (11) (1982) 1163–1184]. The diffusion coefficients of the system are not equal. We prove existence of a wave front solution which connects two nonzero restpoints of the system. In the proof, we rely essentially on the results of Kolmogorov et al. [A study of diffusion with increase in the quantity of matter, and its application to a biological problem, Bull. Moscow State Univ. 17 (1937) 1–72]. We also estimate the wave speed.