Stackelberg-Nash exact controllability for the Kuramoto-Sivashinsky equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Carreno, N.¹  Santos, M. C.² 

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Casilla 110-V, Valparaiso, Chile

[2] Univ Fed Paraiba, Dept Matemat, BR-58051085 Joao Pessoa, Paraiba, Brazil

关键词: Kuramoto-Sivashinsky equation;    Null controllability;    Carleman inequalities;    Hierarchical controls;   

DOI  :  10.1016/j.jde.2018.10.043

来源: Elsevier

【 摘 要 】

This paper deals with a hierarchical control problem for the Kuramoto-Sivashinsky equation following a Stackelberg-Nash strategy. We assume that there is a main control, called the leader, and two secondary controls, called the followers. The leader tries to drive the solution to a prescribed target and the followers intend to be a Nash equilibrium for given functionals. It is known that this problem is equivalent to a null controllability result for an optimality system consisting of three non-linear equations. One of the novelties is a new Carleman estimate for a fourth-order equation with right-hand sides in Sobolev spaces of negative order, which allows to relax some geometric conditions for the observation sets for the followers. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free