Invasive-invaded system of non-Lipschitz porous medium equations with advection

This work provides analytical results towards applications in the field of invasive-invaded systems modeled with nonlinear diffusion and advection. The focus on showing regularity, existence uniqueness weak solutions using condition a slightly positive parabolic operator reaction-absorption monotone properties. coupling terms, that characterizes species interaction, impedes formulation global comparison principle is shown to exist locally. Additionally, this obtained as selfsimilar minimal maximal profiles. A propagating diffusive front until invaded specie notes invasive. When desertion starts, vanishes globally concentrates only tail which exhibits finite speed. Finally, exhibit an exponential decay along characteristic curve. Such not trivial case confirms invasive continues feed during desertion.