|Time:||Apr. 12, 2016, 10:00pm-11:00pm.|
|Place:||216 McAllister Building.|
|Speaker:||Andrea Corli, Department of Mathematics and Computer Science, University of Ferrara|
|Title:||Traveling wave solutions for models of collective movements with degenerate diffusivities.|
The talk deals with a nonhomogeneous scalar parabolic equation with possibly degenerate diffusion term; the process has one stationary state. The equation can be roughly interpreted as modeling collective movements (crowd dynamics, for instance). Existence of semi-wavefront solutions for every wave speed is established and their properties are investigated. Then, a family of traveling wave solutions is constructed by a suitable combination of the previous semi-wavefront solutions. Several extensions of the model are then discussed. Proofs exploit comparison-type techniques.