Dynamics of Partial Differential Equations

Volume 13 (2016)

Number 4

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

Pages: 297 – 331

DOI: https://dx.doi.org/10.4310/DPDE.2016.v13.n4.a2

Authors

Andrea Corli (Department of Mathematics and Computer Science, University of Ferrara, Italy)

Luisa Malaguti (Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Italy)

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 show the existence of semi-wavefront solutions for every wave speed; their properties are investigated. Proofs exploit comparison-type techniques and are carried out in the case of one spatial variable; the extension to the general case is straightforward.

Keywords

degenerate parabolic equations, semi-wavefront solutions, collective movements, crowd dynamics

2010 Mathematics Subject Classification

35C07, 35K55, 35K57, 35K65

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Published 16 December 2016