Sharp forced waves of degenerate diffusion equations in shifting environments

This article is concerned with the sharp forced waves for degenerate diffusion equations in a shifting environment. The degeneracy of diffusion usually causes the forced waves to become sharp. We show that such sharp forced waves exist when the environment improves and propagates with slow speed. To handle the nonautonomous term caused by the shifting environment, we develop a phase transform method to show existence and nonexistence results of nonautonomous and degenerate second-order differential equations.