Séminaire d'AnalyseSingular traveling waves and non-linear reaction-diffusion equations.
jeudi 12 octobre 2017 10:45 - Tours - Salle 1180 (Bât E2)
Linear reaction-diffusion equations have become a very popular tool in the field of Mathematical Biology since the pioneering works of Fisher, Kolmogorov, Petrovski and Piscounov on traveling wave solutions. Despite their large degree of success, these models are not always the most accurate choice due to their exponential tails. We review some alternative descriptions, focusing on certain nonlinear reaction-diffusion equations whose traveling wave solutions come with a natural cutoff; this feature may render such solutions more accurate than the usual ones for some modeling purposes. The analysis of these families of traveling waves is accomplished through a combination of techniques from planar dynamical systems and parabolic-hyperbolic partial differential equations.