Simultaneous identification of the unknown source term and initial value for the time fractional diffusion equation with local and nonlocal operators

Li Qiao, Fan Yang and Xiaoxiao Li

Chaos, Solitons & Fractals, 2024, vol. 189, issue P1

Abstract: In this paper, the problem of simultaneously identifying the unknown source term and initial value for the time fractional diffusion equation with local and nonlocal operators is studied. We prove the problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the measurable data. A fractional Tikhonov regularization method is proposed to solve the inverse problem. Moreover, based on a-priori bound assumption and a-priori, a-posteriori regularization parameter choice rules, we derive the convergence estimates. Finally, we provide several numerical examples to show the effectiveness of the proposed method.

Keywords: Simultaneous identification; Time fractional diffusion equation with local and nonlocal operators; Ill-posed; Regularization method; Convergent estimate (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924011536

DOI: 10.1016/j.chaos.2024.115601

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