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Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements
Author(s) -
Triet Nguyen Anh,
Binh Tran Thanh,
Phuong Nguyen Duc,
Baleanu Dumitru,
Can Nguyen Huu
Publication year - 2021
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.7102
Subject(s) - mathematics , truncation (statistics) , truncation error , noise (video) , rate of convergence , convergence (economics) , hadamard transform , diffusion , work (physics) , initial value problem , value (mathematics) , random noise , nonparametric statistics , mathematical analysis , mathematical optimization , statistics , computer science , physics , artificial intelligence , image (mathematics) , thermodynamics , mechanical engineering , computer network , channel (broadcasting) , engineering , economics , economic growth
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.