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

2017/02/16 by Andrea Corli, Corli, Andrea, Luisa Malaguti +1
Mathematics · #35C07 #35K55 #35K55 (Secondary) #35K57 35K65 #35K57 35K65 (Primary) #35K65 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35C07 #msc:35K55 #msc:35K57 #msc:35K65

paper · pdf · doi:10.48550/arxiv.1702.04884

37 pages

arxiv created 2017/02/16 · arxiv updated 2017/02/17

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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