Simultaneous inversion of two initial values for a time‐fractional diffusion‐wave equation. Issue 1 (5th September 2020)

• Record Type: Journal Article
• Authors: Zhang, Yun; Wei, Ting; Zhang, Yuan‐Xiang
• Is Part Of: Numerical methods for partial differential equations. Volume 37:Issue 1(2021)
• Page Start: 24
• Page End: 43
• Publication Date: 2020-09-05
• Subjects: inverse initial value problem -- iterative Tikhonov regularization method -- time‐fractional diffusion‐wave equation -- uniqueness; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22517
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: This study is devoted to recovering two initial values for a time‐fractional diffusion‐wave equation from boundary Cauchy data. We provide the uniqueness result for recovering two initial values simultaneously by the method of Laplace transformation and analytic continuation. And then we use a nonstationary iterative Tikhonov regularization method to solve the inverse problem and propose a finite dimensional approximation algorithm to find good approximations to the initial values. Numerical examples in one‐ and two‐dimensional cases are provided to show the effectiveness of the proposed method.