Browsing by Author "Triet, Nguyen Anh"

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Citation Count: Triet, Nguyen Anh...et al. (2021). "Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements", Mathematical Methods in the Applied Sciences, Vol. 44, No. 6, pp. 5188-5209.
Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements
(2021) Triet, Nguyen Anh; Binh, Tran Thanh; Phuong, Nguyen Duc; Baleanu, Dumitru; Can, Nguyen Huu; 56389
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.
Citation Count: Triet, Nguyen Anh...et al. (2020). "Regularization of a terminal value problem for time fractional diffusion equation", Mathematical Methods in the Applied Sciences, Vol. 43, No. 6, pp. 3850-3878.
Regularization of a terminal value problem for time fractional diffusion equation
(2020) Triet, Nguyen Anh; Au, Vo Van; Long, Le Dinh; Baleanu, Dumitru; Tuan, Nguyen Huy; 56389
In this article, we study an inverse problem with inhomogeneous source to determine an initial data from the time fractional diffusion equation. In general, this problem is ill-posed in the sense of Hadamard, so the quasi-boundary value method is proposed to solve the problem. In the theoretical results, we propose a priori and a posteriori parameter choice rules and analyze them. Finally, two numerical results in the one-dimensional and two-dimensional case show the evidence of the used regularization method.