Browsing by Author "Nguyen Hoang Luc"

Now showing 1 - 10 of 10

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: 7
Citation - Scopus: 8
Determination of source term for the fractional Rayleigh-Stokes equation with random data
(Springeropen, 2019) Tran Thanh Binh; Baleanu, Dumitru; Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen-H Can; 56389; Matematik
In this article, we consider the problem of finding a source term of a Rayleigh-Stokes equation. Our problem is not well-posed in the sense of Hadamard. The sought solution does not depend continuously on the given data. Using the truncation method and some new techniques on trigonometric estimators, we give the regularized solution. Moreover, the mean square error and convergence rates are established.
Citation - WoS: 7
Citation - Scopus: 7
Identifying the initial condition for space-fractional sobolev equation
(Wilmington Scientific Publisher, Llc, 2021) Nguyen Hoang Luc; Baleanu, Dumitru; Le Dinh Long; Le Thi Diem Hang; Baleanu, Dumitru; Nguyen Huu Can; 56389; Matematik
In this work, a final value problem for a fractional pseudo-parabolic equation is considered. Firstly, we present the regularity of solution. Secondly, we show that this problem is ill-posed in Hadamard's sense. After that we use the quasi-boundary value regularization method to solve this problem. To show that the proposed theoretical results are appropriate, we present an illustrative numerical example.
Citation - WoS: 19
Citation - Scopus: 23
Identifying the space source term problem for a generalization of the fractional diffusion equation with hyper-Bessel operator
(Springer, 2020) Nguyen Hoang Luc; Baleanu, Dumitru; Le Nhat Huynh; Baleanu, Dumitru; Nguyen Huu Can; 56389; Matematik
In this paper, we consider an inverse problem of identifying the source term for a generalization of the time-fractional diffusion equation, where regularized hyper-Bessel operator is used instead of the time derivative. First, we investigate the existence of our source term; the conditional stability for the inverse source problem is also investigated. Then, we show that the backward problem is ill-posed; the fractional Landweber method and the fractional Tikhonov method are used to deal with this inverse problem, and the regularized solution is also obtained. We present convergence rates for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. Finally, we present a numerical example to illustrate the proposed method.
Citation - WoS: 7
Citation - Scopus: 16
Identifying the Space Source Term Problem for Time-Space Diffusion Equation
(Springer, 2020) Karapinar, Erdal; Kumar, Devendra; Sakthivel, Rathinasamy; Nguyen Hoang Luc; Can, N. H.
In this paper, we consider an inverse source problem for the time-space-fractional diffusion equation. Here, in the sense of Hadamard, we prove that the problem is severely ill-posed. By applying the quasi-reversibility regularization method, we propose by this method to solve the problem (1.1). After that, we give an error estimate between the sought solution and regularized solution under a prior parameter choice rule and a posterior parameter choice rule, respectively. Finally, we present a numerical example to find that the proposed method works well.
Citation - WoS: 20
Citation - Scopus: 23
Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel
(Springer, 2020) Nguyen Huu Can; Baleanu, Dumitru; Nguyen Hoang Luc; Baleanu, Dumitru; Zhou, Yong; Le Dinh Long; 56389; Matematik
In this work, we study the problem to identify an unknown source term for the Atangana-Baleanu fractional derivative. In general, the problem is severely ill-posed in the sense of Hadamard. We have applied the generalized Tikhonov method to regularize the instable solution of the problem. In the theoretical result, we show the error estimate between the regularized and exact solutions with a priori parameter choice rules. We present a numerical example to illustrate the theoretical result. According to this example, we show that the proposed regularization method is converged.
Citation - WoS: 3
Citation - Scopus: 3
On a Kirchhoff diffusion equation with integral condition
(Springer, 2020) Danh Hua Quoc Nam; Baleanu, Dumitru; Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen Huu Can; 56389; Matematik
This paper is devoted to Kirchhoff-type parabolic problem with nonlocal integral condition. Our problem has many applications in modeling physical and biological phenomena. The first part of our paper concerns the local existence of the mild solution in Hilbert scales. Our results can be studied into two cases: homogeneous case and inhomogeneous case. In order to overcome difficulties, we applied Banach fixed point theorem and some new techniques on Sobolev spaces. The second part of the paper is to derive the ill-posedness of the mild solution in the sense of Hadamard.
Citation - WoS: 65
Citation - Scopus: 63
On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems
(Springer, 2021) Karapinar, Erdal; Karapınar, Erdal; Ho Duy Binh; Nguyen Hoang Luc; Nguyen Huu Can; 19184; Matematik
In this work, we study an initial value problem for a system of nonlinear parabolic pseudo equations with Caputo fractional derivative. Here, we discuss the continuity which is related to a fractional order derivative. To overcome some of the difficulties of this problem, we need to evaluate the relevant quantities of the Mittag-Leffler function by constants independent of the derivative order. Moreover, we present an example to illustrate the theory.
Citation - WoS: 6
Citation - Scopus: 8
Recovering the space source term for the fractional-diffusion equation with Caputo–Fabrizio derivative
(Springer, 2021) Le Nhat Huynh; Baleanu, Dumitru; Nguyen Hoang Luc; Baleanu, Dumitru; Le Dinh Long; 56389; Matematik
This article is devoted to the study of the source function for the Caputo-Fabrizio time fractional diffusion equation. This new definition of the fractional derivative has no singularity. In other words, the new derivative has a smooth kernel. Here, we investigate the existence of the source term. Through an example, we show that this problem is ill-posed (in the sense of Hadamard), and the fractional Landweber method and the modified quasi-boundary value method are used to deal with this inverse problem and the regularized solution is also obtained. The convergence estimates are addressed for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. In addition, we give a numerical example to illustrate the proposed method.
Citation - WoS: 0
Citation - Scopus: 0
Regularized solution for nonlinear elliptic equations with random discrete data
(Wiley, 2019) Nguyen Duc Phuong; Baleanu, Dumitru; Nguyen Huy Tuan; Baleanu, Dumitru; Nguyen Hoang Luc; 56389; Matematik
The aim of this paper is to study the Cauchy problem of determining a solution of nonlinear elliptic equations with random discrete data. A study showing that this problem is severely ill posed in the sense of Hadamard, ie, the solution does not depend continuously on the initial data. It is therefore necessary to regularize the in-stable solution of the problem. First, we use the trigonometric of nonparametric regression associated with the truncation method in order to offer the regularized solution. Then, under some presumption on the true solution, we give errors estimates and convergence rate in L-2-norm. A numerical example is also constructed to illustrate the main results.