Determining damping terms in fractional wave equations. (1st July 2022)

• Record Type: Journal Article
• Authors: Kaltenbacher, Barbara; Rundell, William
• Is Part Of: Inverse problems. Volume 38:Number 7(2022)
• Publication Date: 2022-07-01
• Subjects: inverse problem -- multiterm fractional PDE -- fractionally damped wave equation; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac6b31
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems that provide relations between the asymptotic behaviour of solutions in time and Laplace domains. The possibility of additionally recovering space-dependent coefficients or initial data is discussed. The resulting methods for reconstructing coefficients and fractional orders in these terms are tested numerically. In addition, we provide an analysis of the forward problem consisting of a multiterm fractional wave equation.