Unknown source identification problem for space-time fractional diffusion equation: optimal error bound analysis and regularization method

2021 ◽  
pp. 1-45
Author(s):  
Fan Yang ◽  
Qian-Chao Wang ◽  
Xiao-Xiao Li
Keyword(s):  
Diffusion Equation ◽  
Source Identification ◽  
Regularization Method ◽  
Identification Problem ◽  
Fractional Diffusion ◽  
Optimal Error ◽  
Time Fractional Diffusion Equation ◽  
Error Bound Analysis ◽  
Optimal Error Bound ◽  
Bound Analysis

scholarly journals A Point Source Identification Problem for a Time Fractional Diffusion Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xiao-Mei Yang ◽  
Zhi-Liang Deng
Keyword(s):  
Heat Source ◽  
Diffusion Equation ◽  
Point Source ◽  
Source Identification ◽  
Identification Problem ◽  
Fractional Diffusion ◽  
Point Sources ◽  
Fractional Diffusion Equation ◽  
Time Fractional Diffusion Equation ◽  
Unknown Point

An inverse source identification problem for a time fractional diffusion equation is discussed. The unknown heat source is supposed to be space dependent only. Based on the use of Green’s function, an effective numerical algorithm is developed to recover both the intensities and locations of unknown point sources from final measurements. Numerical results indicate that the proposed method is efficient and accurate.

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