Dynamics of Partial Differential Equations
Volume 13 (2016)
Semi-wavefront solutions in models of collective movements with density-dependent diffusivity
Pages: 297 – 331
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.
degenerate parabolic equations, semi-wavefront solutions, collective movements, crowd dynamics
2010 Mathematics Subject Classification
35C07, 35K55, 35K57, 35K65