A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS*

doi:10.1007/s10473-024-0523-2

Abstract

Abstract: In this article, we consider the diffusion equation with multi-term time-fractional derivatives. We first derive, by a subordination principle for the solution, that the solution is positive when the initial value is non-negative. As an application, we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a subdomain. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Key words: fractional diffusion equation, inverse source problem, nonlocal observation observation, uniqueness, Tikhonov regularization

CLC Number:

35K65

Li hu, Zhiyuan li, Xiaona yang. A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS^*[J].Acta mathematica scientia,Series B, 2024, 44(5): 2019-2040.

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References

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A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS^*

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