Wavefronts for Generalized Perona-Malik Equations

We consider a generalization of Perona-Malik equation with reaction and convective terms. By assuming that the reaction is monostable, we prove the existence of regular wavefronts as well as some of their qualitative properties. It turns out that the admissible speeds for subcritical or critical wavefronts form a closed half-line; the threshold cannot be computed explicitly but an estimate is provided. Moreover, the wavefronts are strictly monotone and their slope is bounded by the critical values of the diffusion.