Construction of an optimal background profile for the Kuramoto-Sivashinsky equation using semidefinite programming

Wynn A, Fantuzzi G (2015)

Publication Type: Journal article

Publication year: 2015

Journal

Physics Letters A Elsevier

Book Volume: 379

Pages Range: 23-32

Journal Issue: 1-2

DOI: 10.1016/j.physleta.2014.10.039

Abstract

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.

Authors with CRIS profile

Giovanni Fantuzzi

Involved external institutions

Imperial College London / The Imperial College of Science, Technology and Medicine GB United Kingdom (GB)

How to cite

APA:

Wynn, A., & Fantuzzi, G. (2015). Construction of an optimal background profile for the Kuramoto-Sivashinsky equation using semidefinite programming. Physics Letters A, 379(1-2), 23-32. https://dx.doi.org/10.1016/j.physleta.2014.10.039

MLA:

Wynn, Andrew, and Giovanni Fantuzzi. "Construction of an optimal background profile for the Kuramoto-Sivashinsky equation using semidefinite programming." Physics Letters A 379.1-2 (2015): 23-32.

BibTeX: Download