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.

中文翻译：

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人群动力学中的饱和前沿

我们考虑在一个空间维度上的一种退化的标量抛物型方程，它是磁通饱和的。该方程还包含一个对流项。我们研究行波解的存在性和规律性；特别是，我们表明它们可以是不连续的。通过要求熵条件来恢复唯一性，并且熵解是行波解对方程的消失扩散极限，并且具有附加的非退化扩散。还提供了对人群动力学的应用，这激发了本研究的发展。