Desensitizing controls for semilinear wave equations. (April 2018)

• Record Type: Journal Article
• Authors: Wu, Jieqiong; Zhu, Xianzheng
• Is Part Of: Nonlinear analysis. Volume 169(2018)
• Page Start: 79
• Page End: 93
• Publication Date: 2018-04
• Subjects: Desensitizing control -- Semilinear wave equation -- Unique continuation property; 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.2017.12.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The desensitizing control problems for semilinear wave equations are studied. When the nonlinearity f satisfies lim | s | → ∞ f ( s ) | s | ln 2 | s | = lim | s | → ∞ f ′ ( s ) ln 2 | s | = 0, we obtain the existence of a control which desensitizes the boundary observation. The proof is based on the combination of fixed-point arguments and explicit observability estimates for the linearized wave equation with a potential that depends on both x and t . The work solves the problem proposed by Tebou (2011) in the one-dimensional setting. For the interior observation, we assume that the nonlinearity is globally Lipschitz, under which the existence of ε -desensitizing controls is proved. Our proof is based on the fixed-point arguments and the unique continuation property.