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Identifying initial condition of the Rayleigh‐Stokes problem with random noise
Author(s) -
Nguyen Hoang Luc,
Nguyen Huy Tuan,
Mokhtar Kirane,
Duong Dang Xuan Thanh
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5455
Subject(s) - mathematics , regularization (linguistics) , a priori and a posteriori , rayleigh scattering , exact solutions in general relativity , well posed problem , gaussian noise , gaussian , noise (video) , mathematical analysis , inverse problem , random field , algorithm , statistics , physics , computer science , philosophy , epistemology , quantum mechanics , artificial intelligence , optics , image (mathematics)
We investigate a backward problem for the Rayleigh‐Stokes problem, which aims to determine the initial status of some physical field such as temperature for slow diffusion from its present measurement data. This problem is well‐known to be ill‐posed because of the rapid decay of the forward process. We construct a regularized solution using the filter regularization method in the Gaussian random noise. Under some a priori assumptions on the exact solution, we establish the expectation between the exact solution and the regularized solution in the L 2 and H m norms.