scholarly journals Tikhonov regularization method for identifying the space-dependent source for time-fractional diffusion equation on a columnar symmetric domain

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Fan Yang ◽  
Pan Zhang ◽  
Xiao-Xiao Li ◽  
Xin-Yi Ma
Keyword(s):  
Diffusion Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Symmetric Domain ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Tikhonov Regularization Method ◽  
Time Fractional Diffusion Equation

A quasi-boundary regularization method for identifying the initial value of time-fractional diffusion equation on spherically symmetric domain

2019 ◽  
Vol 27 (5) ◽  
pp. 609-621 ◽  
Author(s):  
Fan Yang ◽  
Ni Wang ◽  
Xiao-Xiao Li ◽  
Can-Yun Huang
Keyword(s):  
Diffusion Equation ◽  
Regularization Method ◽  
Regularization Parameter ◽  
A Priori ◽  
Symmetric Domain ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Spherically Symmetric ◽  
Initial Value ◽  
Time Fractional Diffusion Equation

Abstract In this paper, an inverse problem to identify the initial value for high dimension time fractional diffusion equation on spherically symmetric domain is considered. This problem is ill-posed in the sense of Hadamard, so the quasi-boundary regularization method is proposed to solve the problem. The convergence estimates between the regularization solution and the exact solution are presented under the a priori and a posteriori regularization parameter choice rules. Numerical examples are provided to show the effectiveness and stability of the proposed method.

Inverse space-dependent source problem for a time-fractional diffusion equation by an adjoint problem approach

2019 ◽  
Vol 27 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Xiong Bin Yan ◽  
Ting Wei
Keyword(s):  
Diffusion Equation ◽  
Tikhonov Regularization ◽  
Direct Problem ◽  
Fractional Diffusion ◽  
Adjoint Problem ◽  
Fractional Diffusion Equation ◽  
Gradient Algorithm ◽  
Tikhonov Regularization Method ◽  
Series Expression ◽  
Time Fractional Diffusion Equation

AbstractIn this paper, we consider an inverse space-dependent source problem for a time-fractional diffusion equation by an adjoint problem approach; that is, to determine the space-dependent source term from a noisy final data. Based on the series expression of the solution for the direct problem, we improve the regularity of the weak solution for the direct problem under strong conditions, and we provide the existence and uniqueness for the adjoint problem. Further, we use the Tikhonov regularization method to solve the inverse source problem and provide a conjugate gradient algorithm to find an approximation to the minimizer of the Tikhonov regularization functional. Numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document