CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

September 15, 2020 from 10:00 to 11:00 (Montreal/EST time) Zoom meeting

Validating Hopf bifurcations in the Kuramoto-Sivashinsky PDE

Seminar presented by 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.