Identification of Source Term for the Time-Fractional Diffusion-Wave Equation by Fractional Tikhonov Method

Le Dinh Long, Nguyen Hoang Luc, Yong Zhou and and Can Nguyen
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Le Dinh Long: Faculty of Natural Sciences, Thu Dau Mot University, Thu Dau Mot City 820000, Binh Duong Province, Vietnam
Nguyen Hoang Luc: Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
Yong Zhou: Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
and Can Nguyen: Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam

Mathematics, 2019, vol. 7, issue 10, 1-24

Abstract: In this article, we consider an inverse problem to determine an unknown source term in a space-time-fractional diffusion equation. The inverse problems are often ill-posed. By an example, we show that this problem is NOT well-posed in the Hadamard sense, i.e., this problem does not satisfy the last condition-the solution’s behavior changes continuously with the input data. It leads to having a regularization model for this problem. We use the Tikhonov method to solve the problem. In the theoretical results, we also propose a priori and a posteriori parameter choice rules and analyze them.

Keywords: fractional diffusion-wave equation; fractional derivative; ill-posed problem; Tikhonov regularization method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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