Mokhtar Kirane, Bessem Samet, Berikbol T. Torebek
Abstract:
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 |
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Bessem Samet Department of Mathematics College of Science, King Saud University P.O. Box 2455, Riyadh, 11451, Saudi Arabia email: bsamet@ksu.edu.sa |
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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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