Recovery of the time-dependent source term in the stochastic fractional diffusion equation with heterogeneous medium
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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.
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