A5064929276- Fractional Differential Equations Solutions
- Numerical methods in inverse problems
- Numerical methods in engineering
- Nonlinear Differential Equations Analysis
- Differential Equations and Numerical Methods
- Advanced Mathematical Modeling in Engineering
- Differential Equations and Boundary Problems
- Iterative Methods for Nonlinear Equations
- Thermoelastic and Magnetoelastic Phenomena
- Composite Material Mechanics
- Stability and Controllability of Differential Equations
Ho Chi Minh University of Banking
2022-2024
Duy Tan University
2019-2021
Vietnam National University Ho Chi Minh City
2016-2019
Ho Chi Minh City University of Transport
2017-2019
Ho Chi Minh City University of Science
2018
Abstract In this paper, a backward diffusion problem for space-fractional equation (SFDE) with nonlinear source in strip is investigated. This obtained from the classical by replacing second-order space derivative Riesz–Feller of order <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>γ</m:mi> <m:mo>∈</m:mo> <m:mo>(</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mn>2</m:mn> <m:mo>]</m:mo> </m:mrow> </m:math> {\gamma\in(0,2]} . We show that such severely ill-posed and further...
In this paper, we consider a Riesz–Feller space‐fractional backward diffusion problem with time‐dependent coefficient urn:x-wiley:mma:media:mma4284:mma4284-math-0001 We show that is ill‐posed; therefore, propose convolution regularization method to solve it. New error estimates for the regularized solution are given under priori and posteriori parameter choice rules, respectively. Copyright © 2016 John Wiley & Sons, Ltd.
The aim of this paper is to investigate an inverse problem recovering a space-dependent source term governed by distributed order time-fractional diffusion equations in Hilbert scales. Such ill-posed and has important practical applications. For problem, we propose general regularization method based on the idea filter method. With suitable condition, prove that optimal under various choices parameter. One priori parameter choice rule another one discrepancy principle. Finally, capabilities...
Abstract In this paper, we consider the backward diffusion problem for a space-fractional equation (SFDE) with nonlinear source, that is, to determine initial data from noisy final data. Very recently, some papers propose new modified regularization solutions solve problem. To get convergence estimate, they required strongly smooth conditions on exact solution. shall release and introduce stepwise method A numerical example is presented illustrate our theoretical result.
<p style='text-indent:20px;'>In this paper, we deal with the backward problem for nonlinear parabolic equations involving a pseudo-differential operator in <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula>-dimensional space. We prove that is ill-posed sense of Hadamard, i.e., solution, if it exists, does not depend continuously on data. To regularize problem, propose two modified versions so-called optimal...
This article is devoted to solving a backward problem for general nonlinear parabolic equations in Sobolev spaces. The hardly solved by computation since it severely ill‐posed Hadamard's sense. Using the Fourier transform and truncation of high‐frequency components, we construct regularized solution from data given inexactly. As usual problems, rate convergence can be obtained under additional smoothness assumptions on regularity exact solution, so‐called source conditions. By using...
In the present paper, we consider a backward problem for space-fractional diffusion equation (SFDE) with time-dependent coefficient. Such is obtained from classical by replacing second-order spatial derivative Riesz-Feller of order α∈(0,2]. This ill-posed, i.e., solution (if it exists) does not depend continuously on data. Therefore, propose one new regularization to solve it. Then, convergence estimate under priori bound assumptions exact solution.