Some inverse problems for wave equations with fractional derivative attenuation. (1st March 2021)

• Record Type: Journal Article
• Authors: Kaltenbacher, Barbara; Rundell, William
• Is Part Of: Inverse problems. Volume 37:Number 4(2021)
• Publication Date: 2021-03-01
• Subjects: fractionally damped wave equation -- photoacoustic tomography -- inverse problems; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abe136
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The damped wave equation with the attenuation proportional to velocity is ubiquitous in science and engineering and a common situation is when the attenuation depends on frequency. The usual way to incorporate this effect is to introduce fractional order derivatives either as a replacement for u t or as modifier through a spatial component with space fractional derivatives. Models for these are very well developed and the effort in this paper is towards the analysis of the inverse problem of recovering critical coefficients or initial states although we also develop constructive methods for these and analyse their degree of ill-conditioning.