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

Keywords

• traveling-wave solutions
• entropic solutions
• nonlinear convection-diffusion equations
• 35k65
• 35c07
• 35k57