Conference abstracts

Session B1 - Computational Dynamics

July 14, 17:30 ~ 18:00

Symbolic dynamics for Kuramoto-Sivashinsky PDE on the line --- a computer-assisted proof

Piotr Zgliczy\'nski

Jagiellonian University, Krakow, Poland   -   umzglicz@cyf-kr.edu.pl

The Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and with parameter $\nu=0.1212$ is considered. We give a computer-assisted proof the existence of symbolic dynamics and countable infinity of periodic orbits with arbitrary large periods.

The proof is based on the covering relations, the apparent existence of trannsversal heteroclinic connections between two periodic orbits and a new algorithm on rigorous intagration of dissipative PDEs based on the automatic differentiation.

Joint work with Daniel Wilczak (Jagiellonian University, Krakow, Poland).

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