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

In this paper, we consider an inverse problem for a time-fractional diffusion equation in a one-dimensional semi-infinite domain. The temperature and heat flux are sought from a measured temperature history at a fixed location inside the body. We show that such problem is severely ill-posed and furt...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 378; no. 2; pp. 418 - 431
Main Authors: Zheng, G.H., Wei, T.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 15.06.2011
Elsevier
Subjects:
Caputo's fractional derivatives
Exact sciences and technology
Fourier transform
Heat flux
Laplace transform
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Numerical linear algebra
Numerical methods in probability and statistics
Real functions
Regularization method
Sciences and techniques of general use
Temperature
Regularization method
Fourier transform
Temperature
Laplace transform
Caputo's fractional derivatives
Heat flux
Fourier transformation
Fourier analysis
Numerical method
Bounded solution
Convergence
Inverse problem
Exact solution
One-dimensional calculations
Mathematical analysis
Diffusion equation
Ill posed problem
Laplace transformation
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:In this paper, we consider an inverse problem for a time-fractional diffusion equation in a one-dimensional semi-infinite domain. The temperature and heat flux are sought from a measured temperature history at a fixed location inside the body. We show that such problem is severely ill-posed and further apply a new regularization method to solve it based on the solution given by the Fourier method. Convergence estimates are presented under the a priori bound assumptions for the exact solution. Finally, numerical examples are given to show that the proposed numerical method is effective.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.01.067