Boundary Controllability of a Simplified Stabilized Kuramoto-Sivashinsky System

In this paper, we study the controllability of a nonlinear system of coupled second- and fourth-order parabolic equations. This system can be regarded as a simplification of the well-known stabilized Kuramoto-Sivashinsky system. Using only one control applied on the boundary of the second-order equa...

Full description

Saved in:
Bibliographic Details
Published inActa applicandae mathematicae Vol. 188; no. 1; p. 17
Main Authors Hernández-Santamaría, Víctor, Mercado, Alberto, Visconti, Piero
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2023
Springer Nature B.V
Subjects
Applications of Mathematics
Boundary control
Calculus of Variations and Optimal Control; Optimization
Computational Mathematics and Numerical Analysis
Controllability
Diffusion coefficient
Dissolution
Mathematics
Mathematics and Statistics
Nonlinear systems
Parabolic differential equations
Partial Differential Equations
Probability Theory and Stochastic Processes
35K41
Parabolic system
93C20
93B05
Boundary controllability
Source term method
Online AccessGet full text

Cover

More Information
Summary:In this paper, we study the controllability of a nonlinear system of coupled second- and fourth-order parabolic equations. This system can be regarded as a simplification of the well-known stabilized Kuramoto-Sivashinsky system. Using only one control applied on the boundary of the second-order equation, we prove that the local-null controllability of the system holds if the square root of the diffusion coefficient of the second-order equation is an irrational number with finite Liouville-Roth constant.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-023-00626-x