Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements
In this work, we study the final value problem for a system of parabolic diffusion equations. In which, the final value functions are derived from a random model. This problem is severely ill‐posed in the sense of Hadamard. By nonparametric estimation and truncation methods, we offer a new regulariz...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2021-04, Vol.44 (6), p.5188-5209 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Triet, Nguyen Anh Binh, Tran Thanh Phuong, Nguyen Duc Baleanu, Dumitru Can, Nguyen Huu |
| description | In this work, we study the final value problem for a system of parabolic diffusion equations. In which, the final value functions are derived from a random model. This problem is severely ill‐posed in the sense of Hadamard. By nonparametric estimation and truncation methods, we offer a new regularized solution. We also investigate an estimate of the error and a convergence rate between a mild solution and its regularized solutions. Finally, some numerical experiments are constructed to confirm the efficiency of the proposed method. |
| doi_str_mv | 10.1002/mma.7102 |
| format | Article |
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| language | eng |
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| source | Wiley Online Library All Journals |
| subjects | Error analysis Ill‐posed problem Nonlocal diffusion Random noise Regularized solution |
| title | Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements |
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