Insensitizing controls for a phase field system. (September 2016)

• Record Type: Journal Article
• Authors: Calsavara, Bianca M.R.; Carreño, Nicolás; Cerpa, Eduardo
• Is Part Of: Nonlinear analysis. Volume 143(2016)
• Page Start: 120
• Page End: 137
• Publication Date: 2016-09
• Subjects: 82B26 -- 93C20 -- 93B05; Phase field system -- Parabolic system -- Insensitizing controls -- Carleman inequalities; 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.2016.05.008
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, a nonlinear parabolic system modeling phase field phenomena is considered. This system consists of two coupled parabolic equations, the first one describes the temperature of the material and the second one describes a phase field function. Under small perturbations of the initial data, we study the existence of controls insensitizing the phase field function and acting only on the temperature equation. This problem is equivalent to the null controllability of a parabolic system, which is studied by means of duality arguments, Carleman estimates, and fixed point theorems.