Validating Hopf bifurcations in the Kuramoto-Sivashinsky PDE

Séminaire CRM CAMP In Nonlinear Analysis Seminar (15 sept. 2020 / Sept. 15, 2020)

Elena Queirolo (Rutgers University, USA)
Validating Hopf bifurcations in the Kuramoto-Sivashinsky PDE (vidéoconférence)

Abstract / Résumé :

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.