Semi-wavefront for a Lotka–Volterra competition system with spatio-temporal delay

A Lotka–Volterra competition system with spatio-temporal delay is considered in this paper. We show the model admits nonnegative traveling wave solutions connecting equilibrium [Formula: see text] to some unknown positive steady states (which is also called semi-wavefront) when the wave speed satisfies [Formula: see text], and there exists no such semi-wavefront if [Formula: see text]. Furthermore, when the kernel functions only exist in the interspecies competition terms, the unknown positive steady state is co-existence equilibrium [Formula: see text]. Finally, choosing two special kernel functions, the behavior of unknown steady state is revealed by the MATLAB pdepe solver.