Stackelberg-Nash exact controllability for the Kuramoto-Sivashinsky equation
type: Item
instance of: scholarly article
title: Stackelberg-Nash exact controllability for the Kuramoto-Sivashinsky equation
zbMATH Open document ID: 1411.35143
published in: Journal of Differential Equations
publication date: 2019-03-26T00:00:00Z
review text: The authors study a multi-objective control problem for the Kuramoto-Sivashinsky equation following the hierarchical strategy. It is assumed 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. As is known, the Carleman inequalities play an important role in analysis of controllability of distributed systems. The authors prove a new inequality of this type. Then, they establish the observability inequality and deal with the null controllability of the linear system. Finally, it is shown that the optimality system is locally null controllable using a local inversion argument.
reviewed by: Vyacheslav I. Maksimov
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 35K41
Mathematics Subject Classification ID: 35K58
Mathematics Subject Classification ID: 91A65
Mathematics Subject Classification ID: 93A13
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 7041860
zbMATH Keywords: Kuramoto-Sivashinsky equation
zbMATH Keywords: null controllability
zbMATH Keywords: Carleman inequalities
zbMATH Keywords: hierarchical controls
author: N. Carreño
author: Mauricio C. Santos
MaRDI profile type: Publication
full work available at URL: j.jde.2018.10.043
OpenAlex ID: W2901088389
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Wikidata QID: Q128952067
DOI: 10.1016/J.JDE.2018.10.043
description: scientific article; zbMATH DE number 7041860