Browsing by Author "Au, Vo Van"

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On a problem for the nonlinear diffusion equation with conformable time derivative
(2022) Baleanu, Dumitru; Baleanu, Dumitru; Zhou, Yong; Huu Can, Nguyen; 56389
In this paper, we study a nonlinear diffusion equation with conformable derivative: (Formula presented.), where (Formula presented.). We consider both of the problems: Initial value problem: the solution contains the integral (Formula presented.) (critical as (Formula presented.)). Final value problem: not well-posed (if the solution exists it does not depend continuously on the given data). For the initial value problem, the lack of convergence of the integral I, for (Formula presented.). The existence for the solution is represented. For the final value problem, the Hadamard instability occurs, we propose two regularization methods to solve the nonlinear problem in case the source term is a Lipschitz function. The results of existence, uniqueness and stability of the regularized problem are obtained. We also develop some new techniques on functional analysis to propose regularity estimates of regularized solution.
Regularization of a terminal value problem for time fractional diffusion equation
(2020) Baleanu, Dumitru; 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.