scholarly journals A new regularization method for solving a time-fractional inverse diffusion problem

2011 ◽  
Vol 378 (2) ◽  
pp. 418-431 ◽  
Author(s):  
G.H. Zheng ◽  
T. Wei
Keyword(s):  
Regularization Method ◽  
Diffusion Problem ◽  
Inverse Diffusion

scholarly journals A truncation regularization method for a time fractional diffusion equation with an in-homogeneous source

2018 ◽  
Vol 20 ◽  
pp. 02007
Author(s):  
Luu Vu Cam Hoan ◽  
Ho Duy Binh ◽  
Tran Bao Ngoc
Keyword(s):  
Diffusion Equation ◽  
Regularization Method ◽  
Fourier Method ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Fractional Diffusion Equation ◽  
Ill Posed ◽  
Inverse Diffusion ◽  
Time Fractional Diffusion Equation

In the present paper, we consider a time-fractional inverse diffusion problem with an in-homogeneous source, where data is given at x = 1 and the solution is required in the interval 0 < x < 1. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. We propose a regularization method to solve it based on the solution given by the Fourier method.

Stepwise regularization method for a nonlinear Riesz–Feller space-fractional backward diffusion problem

2019 ◽  
Vol 27 (6) ◽  
pp. 759-775
Author(s):  
Dang Duc Trong ◽  
Dinh Nguyen Duy Hai ◽  
Nguyen Dang Minh
Keyword(s):  
Exact Solution ◽  
Initial Data ◽  
Diffusion Equation ◽  
Regularization Method ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Convergence Estimate ◽  
Nonlinear Source ◽  
Space Fractional Diffusion Equation ◽  
Final Data

Abstract In this paper, we consider the backward diffusion problem for a space-fractional diffusion equation (SFDE) with a nonlinear source, that is, to determine the initial data from a noisy final data. Very recently, some papers propose new modified regularization solutions to solve this problem. To get a convergence estimate, they required some strongly smooth conditions on the exact solution. In this paper, we shall release the strongly smooth conditions and introduce a stepwise regularization method to solve the backward diffusion problem. A numerical example is presented to illustrate our theoretical result.

Quasi-solution approach for a two dimensional nonlinear inverse diffusion problem

2013 ◽  
Vol 219 (23) ◽  
pp. 10956-10960 ◽  
Author(s):  
Yiliang Liu ◽  
Salih Tatar ◽  
Suleyman Ulusoy
Keyword(s):  
Diffusion Problem ◽  
Two Dimensional ◽  
Solution Approach ◽  
Inverse Diffusion

scholarly journals Numerical solution of an inverse diffusion problem for the moisture transfer coefficient in a porous material

2007 ◽  
Vol 41 (2) ◽  
pp. 335-344 ◽  
Author(s):  
I. V. Amirkhanov ◽  
E. Pavlušová ◽  
M. Pavluš ◽  
T. P. Puzynina ◽  
I. V. Puzynin ◽  
...  
Keyword(s):  
Porous Material ◽  
Transfer Coefficient ◽  
Numerical Solution ◽  
Moisture Transfer ◽  
Diffusion Problem ◽  
Moisture Transfer Coefficient ◽  
Inverse Diffusion
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