Monotone reducing mechanism in delayed population model with degenerate diffusion

Abstract

In this paper, we study the monotone reducing mechanism of degenerate diffusion equations with time delay. We show the monotone dependence of critical wave speed on time delay. Due to the complex dynamics arising from degeneracy and time delay, we use a new phase transform approach to analyze the delicate local and global behaviors of critical sharp traveling waves and then derive the comparison of critical speeds.