Electron. J. Differential Equations, Vol. 2017 (2017), No. 257, pp. 1-13.

Determination of an unknown source term temperature distribution for the sub-diffusion equation at the initial and final data

Mokhtar Kirane, Bessem Samet, Berikbol T. Torebek

We consider a class of problems modeling the process of determining the temperature and density of nonlocal sub-diffusion sources given by initial and finite temperature. Their mathematical statements involve inverse problems for the fractional-time heat equation in which, solving the equation, we have to find the an unknown right-hand side depending only on the space variable. The results on existence and uniqueness of solutions of these problems are presented.

Submitted September 17, 2017. Published October 11, 2017.
Math Subject Classifications: 35A09, 34K06.
Key Words: Inverse problem; involution; nonlocal sub-diffusion equation; fractional-time diffusion equation.

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Mokhtar Kirane
LaSIE, Faculté des Sciences
Pole Sciences et Technologies
Universit&eaccute; de La Rochelle
Avenue M. Crepeau, 17042 La Rochelle Cedex, France
email: mkirane@univ-lr.fr
Bessem Samet
Department of Mathematics
College of Science, King Saud University
P.O. Box 2455, Riyadh, 11451, Saudi Arabia
email: bsamet@ksu.edu.sa
Berikbol T. Torebek
Department of Differential Equations
Institute of Mathematics and Mathematical Modeling
125 Pushkin str., 050010 Almaty, Kazakhstan
email: torebek@math.kz

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