Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions. (1st November 2022)

• Record Type: Journal Article
• Authors: Ait Ben Hassi, El Mustapha; Chorfi, Salah-Eddine; Maniar, Lahcen
• Is Part Of: Inverse problems. Volume 38:Number 11(2022)
• Publication Date: 2022-11-01
• Subjects: semilinear parabolic systems -- dynamic boundary conditions -- inverse problem -- Carleman estimate -- Lipschitz stability -- observability; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac91ed
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this work, we study the stable determination of four space-dependent coefficients appearing in a coupled semilinear parabolic system with variable diffusion matrices subject to dynamic boundary conditions which couple intern-boundary phenomena. We prove a Lipschitz stability result for interior and boundary potentials by means of only one observation component, localized in any arbitrary open subset of the physical domain. The proof mainly relies on some new Carleman estimates for dynamic boundary conditions of surface diffusion type.