This paper deals with a nonhomogeneous scalar parabolic equation with possibly degenerate diffusion term; the process has only one stationary state. The equation can be interpreted as modeling collective movements (crowd dynamics, for instance). We first prove the existence of semi-wavefront solutions for every wave speed; their properties are investigated. Then, a family of travelling wave solutions is constructed by a suitable combination of the previous semi-wavefront solutions. Proofs exploit comparison-type techniques and are carried out in the case of one spatial variable; the extension to the general case is straightforward.

中文翻译：

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具有密度相关扩散率的集体运动模型中的半波前解

这篇论文讨论了一个具有可能退化扩散项的非齐次标量抛物线方程；该过程只有一种静止状态。该方程可以解释为对集体运动（例如人群动态）进行建模。我们首先证明了对于每个波速都存在半波前解；他们的性质进行了调查。然后，通过适当组合先前的半波前解决方案来构建一系列行波解决方案。证明利用比较类型的技术，并在一个空间变量的情况下进行；一般情况的扩展很简单。