On inverse problems for piezoelectric equation: stability analysis and numerical method. (31st May 2018)

• Record Type: Journal Article
• Authors: Ding, Yibin; Sun, Yuhui; Xu, Xiang
• Is Part Of: Inverse problems. Volume 34:Number 7(2018:Jul.)
• Publication Date: 2018-05-31
• Subjects: piezoelectric equation -- Carleman estimate -- inverse source problem -- inverse coefficient problem -- stability analysis; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aac3b1
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The main purpose of this work is to study an inverse source and inverse coefficient problem for a piezoelectric equation in one dimension which is of great interest in nanomaterials. Based on Carleman estimates, local Hölder stability estimates for the inverse source and coefficient problem are obtained respectively provided that additional measurement data are given on an interior sub-domain with non-vanishing measure. Furthermore, two numerical algorithms based upon conjugate-gradient method are proposed for the corresponding inverse source and coefficient problems. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithms.