Internal controllability of the Kawahara equation on a bounded domain. (August 2019)

• Record Type: Journal Article
• Authors: Chen, Mo
• Is Part Of: Nonlinear analysis. Volume 185(2019)
• Page Start: 356
• Page End: 373
• Publication Date: 2019-08
• Subjects: 35Q53 -- 93B05; Kawahara equation -- Null controllability -- Carleman estimate; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.03.016
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider the Kawahara equation posed on a bounded interval with a distributed control. First, we establish a Carleman estimate for the Kawahara equation with internal observation. Then, applying this Carleman estimate, we can show that the Kawahara equation is null controllable. Furthermore, we prove the null controllability with constraints on the state for the Kawahara equation.