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arXiv · 1911.00304

Reconstruction of the time-dependent source term in a stochastic fractional diffusion equation

Chan Liu·Jin Wen·Zhidong Zhang
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Abstract

In this work, an inverse problem in the fractional diffusion equation with random source is considered. Statistical moments are used of the realizations of single point observation $u(x_0,t,\omega).$ We build the representation of the solution $u$ in integral sense, then prove some theoretical results as uniqueness and stability. After that, we establish a numerical algorithm to solve the unknowns, where the mollification method is used.

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Chan Liu, Jin Wen, Zhidong Zhang. 2019-11-01. Reconstruction of the time-dependent source term in a stochastic fractional diffusion equation. https://arxiv.org/abs/1911.00304

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