Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements. (12th December 2020) - Triet, Nguyen Anh; Binh, Tran Thanh; Phuong, Nguyen Duc; Baleanu, Dumitru; Can, Nguyen Huu
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.