Saturated Fronts in Crowds Dynamics

Abstract We consider a degenerate scalar parabolic equation, in one spatial dimension, of flux-saturated type. The equation also contains convective term. study the existence and regularity traveling-wave solutions; particular we show that they can be discontinuous. Uniqueness is recovered by requiring an entropy condition, entropic solutions turn out to vanishing-diffusion limits with additional non-degenerate diffusion. Applications crowds dynamics, which motivated present research, are provided.