Existence and stability of traveling waves for $p$-Laplacian equations with time delay

Abstract

We consider the existence and stability of traveling wave solutions for Nicholson's blowflies equation with degenerate $p$-Laplacian diffusion and time delay. Existence results are proved by the monotone iteration method. Furthermore, we prove the existence and regularity of original solution for the time-delayed degenerate Nicholson's blowflies equation via compactness analysis. Finally, we prove the stability and exponential convergence rate of traveling waves by an approximated weighted energy method.