Wavefront solutions to reaction-convection equations with Perona-Malik diffusion

We study a nonlinear reaction-convection equation with a degenerate diffusion of Perona-Malik's type and a monostable reaction term. Under quite general assumptions, we show the presence of wavefront solutions and prove their main properties. In particular, such wavefronts exist for every speed in a closed half-line and we give estimates of the threshold speed. The wavefront profiles are also strictly monotone and their slopes are uniformly bounded by the critical values of the diffusion. (c) 2021 Published by Elsevier Inc.

Automated summary

In this study, wavefront solutions of a nonlinear reaction-convection equation with a degenerate diffusion and a monostable reaction term were examined. It was found that these wavefront solutions exist for every speed in a closed half-line, with estimates of the threshold speed provided. The wavefront profiles were shown to be strictly monotone and their slopes were uniformly bounded by the critical values of the diffusion.