Browsing by Subject "SCATTERING PROBLEM"

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  • Niu, Pingping; Helin, Tapio; Zhang, Zhidong (2020)
    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-posedness, Tikhonov regularization is adopted and some numerical results are displayed.
  • Serov, V.; Tyni, T. (2019)
    We consider an inverse medium problem in two- and three-dimensional cases. Namely, we investigate the problem of reconstruction of unknown compactly supported refractive index (contrast) from L-2 with a fixed positive wave number. The proof is based on the new estimates for the Green-Faddeev function in L-infinity space. The main goal of this work is to prove a uniqueness result in the two- and three-dimensional cases and to discuss some possible constructive methods for solving the problem. Finally, we present some numerical examples to demonstrate the results in two dimensions. Published under license by AIP Publishing.