We present a computational study of a simple finite-dimensional feedback control algorithm for stabilizing solutions of infinite-dimensional dissipative evolution equations such as reaction-diffusion systems, the Navier-Stokes equations and the Kuramoto-Sivashinsky equation. This feedback control scheme takes advantage of the fact that such systems possess finite number of determining parameter...

We present the Girsanov theorem for a non linear Itô equation in an infinite dimensional Hilbert space with a non linearity of polynomial growth and an infinite dimensional additive noise. We assume a condition weaker than Novikov one, as done by Mikulevicius and Rozovskii in the study of more general stochastic PDE’s. The equivalence of the laws of the linear equation and of the non linear equ...

The large scale properties of spatiotemporal chaos in the 2D Kuramoto-Sivashinsky equation are studied using an explicit coarse-graining scheme. A set of intermediate equations are obtained which describe interactions between the small scale structures and the hydrodynamic degrees of freedom. Possible forms of the effective large scale hydrodynamics are constructed and examined. Although a numb...

Abstract In this work, we propose a computationally efficient method for the solution of dynamic constraint optimization problems arising in the context of spatiallydistributed processes governed by highly-dissipative nonlinear partial differential equations (PDEs). The method is based on spatial discretization using combination of the method of weighted residuals with spatially-global basis fu...

When pseudospectral approximations are used for space derivatives, one often encounters spurious eigenvalues. These can lead to severe time stepping difficulties for PDEs. This is especially the case for equations with high order derivatives in space, requiring multiple conditions at one or both boundaries. We note here that a very simple-to-implement fictitious point approach circumvents most ...

This article addresses sampled-data control of 2-D Kuramoto–Sivashinsky equation over a rectangular domain $\Omega$ . We suggest to divide the into notation="LaTeX">$N$ subdomains, where sensors provide spati...