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T1 - An inverse random source problem in a stochastic fractional diffusion equation
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UR - http://hdl.handle.net/10138/326825
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A1 - Niu, Pingping; Helin, Tapio; Zhang, Zhidong
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Y1 - 2020
LA - eng
AB - In this work the authors consider an inverse source problem the stochastic fractional diffusion equation. The interested inverse problem is to reconstruct the unknown spatial functions f and g (the latter up to the sign) in the source by the statistics of the final time data u(x, T). Some direct problem results are proved at first, such as the existence, uniqueness, representation and regularity of the solution. Then a reconstruction scheme for f and g up to the sign is given. To tackle the ill-...
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KW - inverse problem; stochastic fractional diffusion equation; random source; Tikhonov regularization; regularity; partial measurements; correlation based imaging; ANOMALOUS DIFFUSION; SCATTERING PROBLEM; MAXIMUM PRINCIPLE; RANDOM-WALKS; SPACE; 111 Mathematics
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