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RECOVERY OF THE TEMPERATURE DISTRIBUTION IN A MULTILAYER FRACTIONAL DIFFUSION EQUATION

Published online by Cambridge University Press:  20 February 2019

KHIEU T. TRAN
Affiliation:
Faculty of Mathematics and Computer Science, University of Science, Vietnam National University Ho Chi Minh City (VNU-HCM), 227 Nguyen Van Cu street, District 5, Ho Chi Minh City, Vietnam Institute for Computational Science and Technology, Ho Chi Minh City, Vietnam email ttkhieu@gmail.com, Khieu.tt@icst.org.vn
LUAN N. TRAN
Affiliation:
Institute for Computational Science and Technology, Ho Chi Minh City, Vietnam email Luan.tn@icst.org.vn
HONG B. Q. NGUYEN
Affiliation:
UFR Mathématiques, Université de Rennes 1, Beaulieu, Bâtiments 22 et 23, 263 avenue du Général Leclerc, 35042 Rennes CEDEX, France email nguyenquanbahong@gmail.com
KHANH Q. TRA*
Affiliation:
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam email traquockhanh@tdtu.edu.vn

Abstract

We study the inverse boundary value problem for fractional diffusion in a multilayer composite medium. Given data in the right boundary of the second layer, the problem is to recover the temperature distribution in the first layer, which is inaccessible for measurement. The problem is ill-posed and we propose a Fourier spectral approach to achieve Hölder approximations. The convergence analysis is performed in both the $L^{2}$- and $L^{\infty }$-settings.

Type
Research Article
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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Footnotes

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant no. 101.02-2018.312.

References

Fu, C.-L., Xiong, X.-T. and Qian, Z., ‘Fourier regularization for a backward heat equation’, J. Math. Anal. Appl. 331(1) (2007), 472480.10.1016/j.jmaa.2006.08.040CrossRefGoogle Scholar
Iyiola, O. S. and Zaman, F. D., ‘A fractional diffusion equation model for cancer tumor’, AIP Adv. 4(10) (2014), 107121.CrossRefGoogle Scholar
Korbel, J. and Luchko, Y., ‘Modeling of financial processes with a space–time fractional diffusion equation of varying order’, Fract. Calc. Appl. Anal. 19(6) (2016), 14141433.CrossRefGoogle Scholar
Nguyen, D., Hai, D. and Trong, D. D., ‘The backward problem for a nonlinear Riesz–Feller diffusion equation’, Acta Math. Vietnam. 43(3) (2018), 449470.Google Scholar
Roberto Evangelista, L. and Kaminski Lenzi, E., Fractional Diffusion Equations and Anomalous Diffusion (Cambridge University Press, Cambridge, 2018).CrossRefGoogle Scholar
Tuan, N. H., Ngoc, T. B., Tatar, S. and Long, L. D., ‘Recovery of the solute concentration and dispersion flux in an inhomogeneous time fractional diffusion equation’, J. Comput. Appl. Math. 342 (2018), 96118.CrossRefGoogle Scholar
Xiong, X., Guo, H. and Liu, X., ‘An inverse problem for a fractional diffusion equation’, J. Comput. Appl. Math. 236(17) (2012), 44744484.CrossRefGoogle Scholar
Xiong, X. T., Shi, W. X. and Hon, Y. C., ‘A one-dimensional inverse problem in composite materials: regularization and error estimates’, Appl. Math. Model. 39(18) (2015), 54805494.10.1016/j.apm.2015.01.004CrossRefGoogle Scholar
Zheng, G. H. and Wei, T., ‘Spectral regularization method for solving a time-fractional inverse diffusion problem’, Appl. Math. Comput. 218(2) (2011), 396405.Google Scholar
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RECOVERY OF THE TEMPERATURE DISTRIBUTION IN A MULTILAYER FRACTIONAL DIFFUSION EQUATION
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