Applied and Computational Math Seminar: Bifurcations in ODEs and a PDE

Speaker: Elena Queirolo, Rutgers University
Title: Bifurcations in ODEs and a PDE

Abstract: We will use validated numerics to prove the existence of Hopf bifurcations in ODEs and a PDE. Numerical approximation can be proved to be in the neighbourhood of exact solutions thanks to validated numerics, in particular we will talk about the radii polynomial approach. In this talk, we want to use such techniques in combination with rewritings of the definitions of saddle node bifurcation and Hopf bifurcation to prove the existence of such bifurcation in ODE systems. We will then extend these results to PDEs, in particular to the Kuramoto-Sivashinky equation. We present a proof of the existence of a Hopf bifurcation from a non-trivial branch of space-periodic solutions.  

Time: Friday, December 6, 2019, 1:30-2:30pm

Place: Exploratory Hall, Room 4106