CRM CAMP in Nonlinear Analysis

Preuves mathématiques assistées par ordinateur en analyse non linéaire

15 septembre 2020 de 10 h 00 à 11 h 00 (heure de Montréal/HNE) Réunion Zoom

Validating Hopf bifurcations in the Kuramoto-Sivashinsky PDE

Séminaire par Elena Queirolo (Rutgers University, USA)

We prove the existence of a Hopf bifurcation in the Kuramoto–Sivashinsky PDE. For this, we rewrite the Kuramoto–Sivashinsky equation into a desingularized formulation near the Hopf point via a blow-up approach and we apply the radii polynomial approach to validate a solution branch of periodic solutions. Then this solution branch includes the Hopf bifurcation point.