Construction of an optimal background profile for the Kuramoto-Sivashinsky equation using semidefinite programming - Wynn, Andrew; Fantuzzi, Giovanni (Physics Letters A, 2015)
A method to construct systematically an optimal background profile for the Kuramoto-Sivashinsky equation is developed by formulating the classical problem as an optimisation problem. In particular, we show that the infinite-dimensional problem can be rewritten as a finite-dimensional convex semidefinite problem, which is solved to construct a background profile and to obtain an upper bound on the energy of the solution ||u|| that applies to the infinite-dimensional PDE. The results are compared to existing analytical results, and support the fact that limsupt→∞||u||≤bsupesup is the optimal estimate achievable with the background profile method and a quadratic Lyapunov function.
CRIS-Team Scopus Importer:2022-09-26
Keywords: Kuramoto-Sivashinsky; Optimal background profile; Semidefinite programming