76 citations · 669 across the 27 of their papers we have counts for
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math.DS2018★ 16 cited
Bounding extrema over global attractors using polynomial optimisation
David Goluskin
We describe a framework for bounding extreme values of quantities on global attractors of differential dynamical systems. A global attractor is the minimal set that attracts all bo…
math.DS2018★ 46 cited
Bounds on mean energy in the Kuramoto-Sivashinsky equation computed using semidefinite programming
David Goluskin, Giovanni Fantuzzi
We present methods for bounding infinite-time averages in dynamical systems governed by nonlinear PDEs. The methods rely on auxiliary functionals, which are similar to Lyapunov fun…