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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Vydané v:	Journal of mathematical analysis and applications Ročník 378; číslo 2; s. 418 - 431
Hlavní autori:	Zheng, G.H., Wei, T.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier Inc 15.06.2011 Elsevier
Predmet:	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
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Abstract	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.
AbstractList	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.
Author	Zheng, G.H. Wei, T.
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Cites_doi	10.1016/j.jde.2008.10.027 10.1016/j.cnsns.2008.08.004 10.1088/0305-4470/27/10/017 10.1088/0305-4470/25/8/023 10.1137/S1064827597331394 10.1016/0893-9659(96)00089-4 10.1016/S0378-4371(00)00255-7 10.1016/j.camwa.2006.05.027 10.1029/2000WR900032 10.1016/j.camwa.2008.05.015 10.1137/0142040 10.1016/0960-0779(95)80003-Y 10.1088/0305-4470/25/8/024 10.1016/0022-247X(72)90189-8 10.1016/S0370-1573(00)00070-3
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SubjectTerms	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
Title	A new regularization method for solving a time-fractional inverse diffusion problem
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