Sufficient and necessary initial mass conditions for the existence of a waiting time in nonlinear-convection processes

Abstract

We study the initial behavior of the fronts (for interfaces) generated by the solutions of the equation ut = (um)xx + b(uλ)x, where m, b, λ > 0 are real numbers. We prove a mass comparison principle that allows us to give necessary and sufficient conditions in order to have waiting time at the fronts. Different regions in the (λ, m) parameter space must be introduced leading to answer of very different nature.