  The Gatenby-Gawlinski model for cancer invasion is object of analysis in
order to investigate the mathematical framework behind the model working by
means of suitable reductions. We perform numerical simulations to study the
sharpness/smoothness of the traveling fronts starting from a brief overview
about the full model and proceed by examining the case of a two-equations-based
and one-equation-based reduction. We exploit a numerical strategy depending on
a finite volume approximation and employ a space-averaged wave speed estimate
to quantitatively approach the traveling waves phenomenon. Concerning the one
equation-based model, we propose a reduction framed within the degenerate
reaction-diffusion equations field, which proves to be effective in order to
qualitatively recover the typical trends arising from the Gatenby-Gawlinski
model. Finally, we carry out some numerical tests in a specific case where the
analytical solution is available.
