论文标题
时间分数扩散方程的逆随机源问题的数值解通过phaselift
Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift
论文作者
论文摘要
本文涉及随机时间分数扩散方程的反随机源问题，其中假定源是由高斯随机场驱动的。通过检查频域中等效的随机两点边界值问题的解决方案的适当性和规律性，表明直接问题已得到充分序列。对于反问题，事实证明，随机源扩散系数的傅立叶模量是由边界数据的傅立叶变换的方差唯一确定的。作为逆问题的相位检索，使用随机掩模的闪光法来恢复从其傅立叶模量的扩散系数。据报道，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.
