Semi-wavefront solutions in models of collective movements with density-dependent diffusivity

Andrea Corli; Luisa Malaguti

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arXiv · 1702.04884

Semi-wavefront solutions in models of collective movements with density-dependent diffusivity

Andrea Corli·Luisa Malaguti

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Abstract

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.

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Andrea Corli, Luisa Malaguti. 2017-02-16. Semi-wavefront solutions in models of collective movements with density-dependent diffusivity. https://arxiv.org/abs/1702.04884

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