Traveling wave solutions in partially degenerate cooperative reaction–diffusion systems

We study the existence of traveling wave solutions for partially degenerate cooperative reaction–diffusion systems that can have three or more equilibria. We show via integral systems that there exist traveling wave solutions in a partially degenerate reaction–diffusion system with speeds above two well-defined extended real numbers. We prove that the two numbers are the same and may be characterized as the spreading speed as well as the slowest speed of a class of traveling wave solutions provided that the linear determinacy conditions are satisfied. We demonstrate our theoretical results by examining a partially degenerate Lotka–Volterra competition model with advection terms.