Null controllability of the complex Ginzburg–Landau equation

Null Controllability of a Nonlinear Heat Equation

On the minimal time null controllability of the heat equation

In this work, two-dimensional microeconomic models with three controls are created and investigated. The models describe a manufacturer producing a consumer good and a retailer that buys his product in order to resell it for profit. Two types of differential hierarchical games will be applied in order to model the interactions of manufacturer and retailer. We will consider the difficult case in...

Remarks on the null controllability of the Burgers equation

In the context of the Burgers equation with distributed controls, we present optimal estimates for the minimal time of controllability T (r) of the initial data of norm r in L2. To cite this article: E. Fernández-Cara, S. Guerrero, C. R. Acad. Sci. Paris, Ser. I 341 (2005).  2005 Académie des sciences. Published by Elsevier SAS. All rights reserved. Résumé Remarques sur la contrôlabilité exact...

Boundary local null-controllability of the Kuramoto-Sivashinsky equation

We prove that the Kuramoto-Sivashinsky equation is locally controllable in 1D and in 2D with one boundary control. Our method consists in combining several general results in order to reduce the nullcontrollability of this nonlinear parabolic equation to the exact controllability of a linear beam or plate system. This improves known results on the controllability of Kuramoto-Sivashinsky equatio...

Null Controllability and Stabilization of the Linear Kuramoto-sivashinsky Equation

In this article, we study the boundary controllability of the linear Kuramoto-Sivashinsky equation on a bounded interval. The control acts on the first spatial derivative at the left endpoint. First, we prove that this control system is null controllable. It is done using a spectral analysis and the method of moments. Then, we introduce a boundary feedback law stabilizing to zero the solution o...