4.2 Article

Inversion of the Initial Value for a Time-Fractional Diffusion-Wave Equation by Boundary Data

Journal

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
Volume 20, Issue 1, Pages 109-120

Publisher

WALTER DE GRUYTER GMBH
DOI: 10.1515/cmam-2018-0194

Keywords

Fractional Diffusion-Wave Equation; Inverse Initial Value Problem; Uniqueness; Numerical Method

Funding

  1. NSF of China [11371181, 11771192, 11601216]

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In this study, we consider an inverse problem of recovering the initial value for a multi-dimensional time-fractional diffusion-wave equation. By using some additional boundary measured data, the uniqueness of the inverse initial value problem is proven by the Laplace transformation and the analytic continuation technique. The inverse problem is formulated to solve a Tikhonov-type optimization problem by using a finite-dimensional approximation. We test four numerical examples in one- dimensional and two-dimensional cases for verifying the effectiveness of the proposed algorithm.

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