Browsing by Author "Long, Le Dinh"

Now showing 1 - 3 of 3

Citation - WoS: 9
Citation - Scopus: 10
Identifying the Source Function for Time Fractional Diffusion With Non-Local in Time Conditions
(Springer Heidelberg, 2021) Baleanu, Dumitru; Agarwal, Ravi P.; Long, Le Dinh; Luc, Nguyen Hoang
The diffusion equation has many applications in fields such as physics, environment, and fluid mechanics. In this paper, we consider the problem of identifying an unknown source for a time-fractional diffusion equation in a general bounded domain from the nonlocal integral condition. The problem is non-well-posed in the sense of Hadamard, i.e, if the problem has only one solution, the solution will not depend continuously on the input data. To get a stable solution and approximation, we need to offer the regularization methods. The first contribution to the paper is to provide a regularized solution using the modified fractional Landweber method. Two choices are proposed including a priori and a posteriori parameter choice rules, to estimate the convergence rate of the regularized methods. The second new contribution is to use truncation to give an estimate of L-p for the convergence rate.
Citation - WoS: 19
Citation - Scopus: 20
An Inverse Source Problem for Pseudo-Parabolic Equation With Caputo Derivative
(Springer Heidelberg, 2022) Luc, Nguyen Hoang; Tatar, Salih; Baleanu, Dumitru; Can, Nguyen Huu; Long, Le Dinh
In this paper, we consider an inverse source problem for a fractional pseudo-parabolic equation. We show that the problem is severely ill-posed (in the sense of Hadamard) and the Tikhonov regularization method is proposed to solve the problem. In addition, we present numerical examples to illustrate applicability and accuracy of the proposed method to some extent.
Citation - WoS: 10
Citation - Scopus: 15
Reconstructing the Right-Hand Side of a Fractional Subdiffusion Equation From the Final Data
(Springeropen, 2020) Baleanu, Dumitru; Long, Le Dinh; Can, Nguyen-Huu; Luc, Nguyen Hoang
In this study, we study an inverse source problem for the time-fractional diffusion equation, where the final data t=Tare given. We show that our problem is ill-posed in the sense of Hadamard. Applying a truncation method, we give the regularized solution. Finally, convergence estimates under a priori and a posteriori parameter choice rules are proved.