DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491