Traveling Fronts for (q,r)‐Relativistic Operators: Existence and Asymptotic Properties

ABSTRACT A new reaction–diffusion model governed by a ‐relativistic type diffusion, generalizing the ‐relativistic one and encompassing singular and/or degenerate diffusivity, is introduced. In the monostable case, some existence results for (decreasing) fronts are then provided, exploiting the study of a suitable two‐point problem obtained from a first‐order reduction. Moreover, the asymptotic properties of such front‐type solutions, in particular their regularity and their sharpness, are studied by means of comparison principles. Some illustrative figures for the deriving scenario are finally shown.