Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements. (12th December 2020)

• Record Type: Journal Article
• Authors: Triet, Nguyen Anh; Binh, Tran Thanh; Phuong, Nguyen Duc; Baleanu, Dumitru; Can, Nguyen Huu
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 6(2021)
• Page Start: 5188
• Page End: 5209
• Publication Date: 2020-12-12
• Subjects: Ill‐posed problem -- Nonlocal diffusion -- Random noise -- Regularized solution; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7102
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.