Variational Regularization of &nbsp;the Inverse Problem of a Class of &nbsp;Nonlinear Time-Fractional Diffusion Equations

LIU Mian; CHENG Hao; SHI Chengxin

doi:10.21656/1000-0887.420168

Volume 43 Issue 3

Mar. 2022

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Article Navigation > Applied Mathematics and Mechanics > 2022 > 43(3): 341-352

LIU Mian, CHENG Hao, SHI Chengxin. Variational Regularization of the Inverse Problem of a Class of Nonlinear Time-Fractional Diffusion Equations[J]. Applied Mathematics and Mechanics, 2022, 43(3): 341-352. doi: 10.21656/1000-0887.420168

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Variational Regularization of the Inverse Problem of a Class of Nonlinear Time-Fractional Diffusion Equations

doi: 10.21656/1000-0887.420168

School of Science, Jiangnan University, Wuxi, Jiangsu 214122, P.R.China

Received Date: 2021-06-17
Rev Recd Date: 2021-08-26

Available Online: 2022-01-08

Publish Date: 2022-03-08

Abstract

Abstract

The nonlinear time-fractional diffusion equations were considered in the 2D domain, and the physical information in initial state
\begin{document}$ u(0,y,t) $\end{document}
of the material was recovered from the measured data in the final state. This problem is seriously ill-posed, that is, the solution to this problem does not continuously depend on the measured data. Therefore, a variational regularization method was proposed to construct the approximate solution to the problem, and the convergence error estimates of the exact and approximate solutions were obtained under the assumption of the priori bounds on the exact solutions. Finally, a numerical example was given to verify the effectiveness of the proposed method.
- time-fractional diffusion equation,
- ill-posed problem,
- variational regularization,
- error estimate

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References(22)

References

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