Results 231 to 240 of about 769,228 (261)

Fourier regularization for a final value time-fractional diffusion problem

Applicable Analysis, 2014
The evolution process of fractional order describes some phenomenon of anomalous diffusion and transport dynamics in complex system. The equation containing time-fractional derivative provides a suitable mathematical model for describing such a process.
Ming Yang, Jijun Liu
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Final value problem for nonlinear time fractional reaction–diffusion equation with discrete data

Journal of Computational and Applied Mathematics, 2020
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Nguyen Huy Tuan, Dumitru Baleanu, Tran Ngoc Thach, Donal O'Regan, Nguyen Huu Can   +4 more
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The final value problem

1987
One of the classical ill-posed problems (in the sense of Hadamard) is the final value problem for evolution equations; a special case of this problem is the solution of the heat equation backwards in time. We consider some regularization methods for this ill-posed problem.
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The final value problem for anomalous diffusion equations involving weak-valued nonlinearities

Journal of Mathematical Analysis and Applications
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Nguyen Thi Van Anh, Tran Dinh Ke, Do Lan
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Generalized Tikhonov method for the final value problem of time-fractional diffusion equation

International Journal of Computer Mathematics, 2015
This paper investigates the final value problem for a time-fractional diffusion equation. We determine the initial data from a noisy final data. A generalized Tikhonov regularization method is proposed to deal with this ill-posed problem, and then the convergence rates is derived by the a-priori and a-posteriori choice rules of regularization parameter.
Hongwu Zhang, Xiaoju Zhang
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On a final value problem for the time-fractional diffusion equation with inhomogeneous source

Inverse Problems in Science and Engineering, 2016
In this paper, we consider an inverse problem for the time-fractional diffusion equation with inhomogeneous source to determine an initial data from the observation data provided at a later time. In general, this problem is ill-posed, therefore we construct a regularizing solution using the quasi-boundary value method.
Nguyen Huy Tuan, Le Dinh Long, Van Thinh Nguyen, Thanh Tran   +3 more
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Solving a final value fractional diffusion problem by boundary condition regularization

Applied Numerical Mathematics, 2013
The evolution process of fractional order describes some phenomenon of anomalous diffusion and transport dynamics in complex system. The equation containing fractional derivatives provides a suitable mathematical model for describing such a process. The initial boundary value problem is hard to solve due to the nonlocal property of the fractional order
Ming Yang, Jijun Liu
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On a final value problem for fractional reaction‐diffusion equation with Riemann‐Liouville fractional derivative

Mathematical Methods in the Applied Sciences, 2019
In this paper, we study a backward problem for a fractional diffusion equation with nonlinear source in a bounded domain. By applying the properties of Mittag‐Leffler functions and Banach fixed point theorem, we establish some results above the existence, uniqueness, and regularity of the mild solutions of the proposed problem in some suitable space ...
Ngoc Tran, Vo Van Au, Yong Zhou, Nguyen Huy Tuan   +3 more
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Existence and uniqueness of mild solutions for a final value problem for nonlinear fractional diffusion systems

Communications in Nonlinear Science and Numerical Simulation, 2019
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Bao Ngoc Tran, Nguyen Huy Tuan, Donal O'Regan   +2 more
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The Accuracy of Approximate Solutions for a Boundary Value Inverse Problem with Final Overdetermination

2019
The paper aims to investigate the accuracy of the methods for approximate solving a boundary value inverse problem with final overdetermination for a parabolic equation. We use the technique of the continuation to the complex domain and the expansion of the unknown function into a Dirichlet series (exponential series) to formulate the inverse problem ...
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