The Role of Convection in the Limit Shape of the Critical Front Profile for Born-Infeld Diffusion Models

In this paper, we deal with models with Born-Infeld (or relativistic ) type diffusion and monostable reaction, investigating the effect of the introduction of a convection term on the limit shape of the critical front profile for vanishing diffusion. We first provide an estimate of the critical speed and then, through a careful analysis of an equivalent first-order problem, we show that different convection terms may lead either to a complete sharpening of the limit profile or to its complete regularization, presenting some related numerical simulations.