Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift
Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift
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DOI：
10.1088/1361-6420/abe6f0
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发表时间：
2020-12
期刊：
影响因子：
2.1
通讯作者：
Yuxuan Gong;Peijun Li;Xu Wang;Xiang Xu
中科院分区：
文献类型：
--
作者：
Yuxuan Gong;Peijun Li;Xu Wang;Xiang Xu
研究了一类随机时间分数阶扩散方程的随机源反问题，其中源被假定为高斯随机场驱动。正问题是适定性的，通过检查的适定性和正则性的解决方案的等效随机两点边值问题在频域中。对于反问题，证明了随机源扩散系数的傅里叶模由边界数据的傅里叶变换的方差唯一确定。作为反问题的相位恢复，随机掩模的相移方法被应用于从其傅立叶模恢复扩散系数。数值实验证明了该方法的有效性。
This paper is concerned with the inverse random source problem for a stochastic time fractional diffusion equation, where the source is assumed to be driven by a Gaussian random field. The direct problem is shown to be well-posed by examining the well-posedness and regularity of the solution for the equivalent stochastic two-point boundary value problem in the frequency domain. For the inverse problem, the Fourier modulus of the diffusion coefficient of the random source is proved to be uniquely determined by the variance of the Fourier transform of the boundary data. As a phase retrieval for the inverse problem, the phaselift method with random masks is applied to recover the diffusion coefficient from its Fourier modulus. Numerical experiments are reported to demonstrate the effectiveness of the proposed method.