Browsing by Author "Nguyen Anh Triet"

Now showing 1 - 3 of 3

Citation - WoS: 5
Citation - Scopus: 5
A Filter Method for Inverse Nonlinear Sideways Heat Equation
(Springer, 2020) Nguyen Anh Triet; Baleanu, Dumitru; O'Regan, Donal; Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen Can; 56389; Matematik
In this paper, we study a sideways heat equation with a nonlinear source in a bounded domain, in which the Cauchy data at x=X are given and the solution in 0 <= x < X is sought. The problem is severely ill-posed in the sense of Hadamard. Based on the fundamental solution to the sideways heat equation, we propose to solve this problem by the filter method of degree alpha, which generates a well-posed integral equation. Moreover, we show that its solution converges to the exact solution uniformly and strongly in L-p(omega,X; L-2 (R)); omega is an element of[0,X) under a priori assumptions on the exact solution. The proposed regularized method is illustrated by numerical results in the final section.
Citation - WoS: 9
Citation - Scopus: 9
Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements
(Wiley, 2021) Nguyen Anh Triet; Baleanu, Dumitru; Tran Thanh Binh; Nguyen Duc Phuong; Baleanu, Dumitru; Nguyen Huu Can; 56389; Matematik
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 - WoS: 20
Regularization of a terminal value problem for time fractional diffusion equation
(Wiley, 2020) Nguyen Anh Triet; Baleanu, Dumitru; Vo Van Au; Le Dinh Long; Baleanu, Dumitru; Nguyen Huy Tuan; 56389; Matematik
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.