Propagation fronts in a simplified model of tumor growth with degenerate cross-dependent self-diffusivity (Q2061551)

This paper performed a complete analysis of existence and non-existence of invasive fronts for the reduced Gatenby-Gawlinski model. The traveling wave profile and its asymptotic states at \(\pm \infty\) are investigated in the regimes are called, respectively, homogeneous invasion and heterogeneous invasion. In both cases, we prove that a propagating front exists whenever the speed parameter \(c\) is strictly positive. We also derive an accurate approximation of the front profile in the singular limit \(c \rightarrow 0.\) This paper also shows that there exists no minimal speed for the propagation fronts of a given system. Finally, all the results are summarized with some conclusions.