Reconstruction of the initial state from the data measured on a sphere for plasma-acoustic wave equations. (3rd August 2018)

• Record Type: Journal Article
• Authors: Bae, Junsik; Kwon, Bongsuk; Moon, Sunghwan
• Is Part Of: Inverse problems. Volume 34:Number 10(2018:Oct.)
• Publication Date: 2018-08-03
• Subjects: wave equation -- Euler–Poisson system -- photoacoustic tomography -- ion-acoustic -- electron-acoustic -- reconstruction; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aad343
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We establish a reconstruction formula for the initial information of a density (pressure) from the time records of data measured on a sphere for a certain class of wave-type equations. We first derive a reconstruction formula of integral form, and by applying the theory of Fourier Bessel series for this, we also obtain a formula of discrete version, which is more robust and numerically advantageous in the presence of noises. The reconstruction formulas we propose in this work are explicit and applicable to a wider class of wave-type equations including the plasma-acoustic wave equations.