论文标题
用异质培养基恢复随机分数扩散方程中时间依赖性源项
Recovery of the time-dependent source term in the stochastic fractional diffusion equation with heterogeneous medium
论文作者
论文摘要
在这项工作中，考虑了与随机源的分数扩散方程中的一个反问题。所使用的测量值是单点数据$ u（x_0，t，ω）实现的统计矩。$我们在整体意义上构建了解决方案$ u $的表示形式，然后证明可以在理论上受到矩的未知数。对于数值重建，我们建立了一种具有正则化Levenberg-Marquardt类型的迭代算法，并显示了该算法产生的一些数值结果。对于高度异构培养基的情况，将采用广义的多尺度有限元方法（GMSFEM）。
In this work, an inverse problem in the fractional diffusion equation with random source is considered. The measurements used are the statistical moments of the realizations of single point data $u(x_0,t,ω).$ We build the representation of the solution $u$ in integral sense, then prove that the unknowns can be bounded by the moments theoretically. For the numerical reconstruction, we establish an iterative algorithm with regularized Levenberg-Marquardt type and some numerical results generated from this algorithm are displayed. For the case of highly heterogeneous media, the Generalized Multiscale finite element method (GMsFEM) will be employed.
