时空分数阶扩散波动方程的初值识别问题

Abstract

Abstract:

In this paper, we study the identification of unknown initial values of time-space fractional diffusion-wave matrix. Firstly, we prove that the problem is ill-posed and give the conditional stability result. Then, we use Tikhonov regularization method to restore the stability of the solutions, and give the convergence error estimates under a priori regularization parameter selection rule and a posteriori regularization parameter selection rule. Finally, numerical examples show that the regularization method is effective.

Key words: Time-space fractional diffusion-wave matrix, Ill-posed problem, Identify unknown initial values, Tikhonov regularization method, Error estimation

CLC Number:

O175

Yang Fan, Cao Ying, Li Xiaoxiao. Identification of Initial Values of Space-Time Fractional Diffusion-Wave Equation[J].Acta mathematica scientia,Series A, 2023, 43(2): 377-398.

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References

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Identification of Initial Values of Space-Time Fractional Diffusion-Wave Equation

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