Computational approaches to PDE dynamics

Jeremy Parker (University of Dundee)

Time:

2PM Tuesday, 4 August 2026

Location:

Science North, N0.20

I will present the Kuramoto-Sivashinsky equation as a model system for more complicated dissipative PDEs which arise in fluid dynamics, and also as an interesting system in its own right. I will present different perspectives for understanding the behaviour of the system, and how these can be implemented computationally. By finding individual periodic and quasiperiodic solutions and the relationships between them, we can build up a local picture in state space of the complicated dynamics. Complementing this, numerically derived bounds using polynomial optimisation give a global perspective.