Finite propagation and saturation in reaction-diffusion-advection equations governed by p-Laplacian operator

The paper concerns front propagation for the following mono-stable reaction-diffusion-advection equation $$f(u)u_x+g(u)u_{\tau }=[d(u)\mathrm{\mid }{u}_x{\mathrm{\mid }}^{p-2}{u}_x{]}_x+\rho (u),(x,\tau )\in \mathbb{R}\times [0,+\mathrm{\infty })\mathrm{.}$$ Besides existence and non-existence results for traveling wave solutions, the main focus is their classification: we provide criteria to establish if they attain one or both the equilibria at a finite time and in this case, if they are continuable as $C^1$-solutions or if they are sharp solutions.