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- Title
Identifying initial condition of the Rayleigh‐Stokes problem with random noise.
- Authors
Nguyen, Hoang Luc; Nguyen, Huy Tuan; Mokhtar, Kirane; Duong Dang, Xuan Thanh
- Abstract
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 L2 and Hm norms.
- Subjects
RANDOM noise theory
- Publication
Mathematical Methods in the Applied Sciences, 2019, Vol 42, Issue 5, p1561
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.5455