On uniqueness and stable estimation of multiple parameters in the Cahn–Hilliard equation. (1st June 2023)

• Record Type: Journal Article
• Authors: Brunk, Aaron; Egger, Herbert; Habrich, Oliver
• Is Part Of: Inverse problems. Volume 39:Number 6(2023)
• Publication Date: 2023-06-01
• Subjects: Cahn–Hilliard system -- parameter identification -- equation error methods -- inverse problems -- Tikhonov regularization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/acca44
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider the identifiability and stable numerical estimation of multiple parameters in a Cahn–Hilliard model for phase separation. Spatially resolved measurements of the phase fraction are assumed to be accessible, with which the identifiability of single and multiple parameters up to certain scaling invariances is established. A regularized equation error approach is proposed for the stable numerical solution of the parameter identification problems, and convergence of the regularized approximations is proven under reasonable assumptions on the data noise. The viability of the theoretical results and the proposed methods is demonstrated in numerical tests.