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Licensed Unlicensed Requires Authentication Published by De Gruyter January 20, 2019

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

  • Suzhen Jiang , Kaifang Liao and Ting Wei EMAIL logo

Abstract

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.

MSC 2010: 65M32; 35R11

Award Identifier / Grant number: 11371181

Award Identifier / Grant number: 11771192

Award Identifier / Grant number: 11601216

Funding statement: This paper was supported by the NSF of China (11371181, 11771192, 11601216).

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Received: 2018-08-02
Revised: 2018-11-21
Accepted: 2018-12-16
Published Online: 2019-01-20
Published in Print: 2020-01-01

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