Bounds on mean energy in the Kuramoto–Sivashinsky equation computed using semidefinite programming

@article{Goluskin2019BoundsOM,
  title={Bounds on mean energy in the Kuramoto–Sivashinsky equation computed using semidefinite programming},
  author={David Goluskin and Giovanni Fantuzzi},
  journal={Nonlinearity},
  year={2019},
  volume={32},
  pages={1705 - 1730}
}
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 functionals but satisfy different inequalities. The inequalities are enforced by requiring certain expressions to be sums of squares of polynomials, and the optimal choice of auxiliary functional is posed as a semidefinite program (SDP) that can be solved computationally. To formulate these SDPs we approximate the PDE by… 
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