Date/heure
16 novembre 2021
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Dongyuan Xiao (Montpellier)
Catégorie d'évènement Séminaire Équations aux Derivées Partielles et Applications (Nancy)
Résumé
We consider the reaction-diffusion competition system
v_t=dv_{xx}+rv(1-v-u),$$
which is the so-called critical case. The associated ODE system then admits infinitely many equilibria, which makes the analysis quite intricate. We first prove the non-existence of monotone traveling waves by applying the phase plane analysis. Next, we study the long-time behavior of the solution of the Cauchy problem with a compactly supported initial datum. We not only reveal that the »faster » species excludes the »slower » species (with an identified »spreading speed »), but also provide a sharp description of the profile of the solution, thus shedding light on a new »bump phenomenon ».