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

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. © 2017 Texas State University.

Authors
Kirane M. 1, 2, 3 , Samet B. 4 , Torebek B.T.5, 6
Journal
Electronic Journal of Differential Equations
Language
English
Status
Published
Link
External link
Number
257
Volume
2017
Year
2017
Organizations
  • 1 LaSIE, Faculté des Sciences, Pole Sciences et Technologies, Université de La Rochelle, Avenue M. Crepeau, La Rochelle Cedex, 17042, France
  • 2 NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
  • 3 RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russian Federation
  • 4 Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia
  • 5 Department of Differential Equations, Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050010, Kazakhstan
  • 6 Al-Farabi Kazakh National University, 71 Al-Farabi ave., Almaty, 050040, Kazakhstan
Keywords
Fractional-time diffusion equation; Inverse problem; Involution; Nonlocal sub-diffusion equation
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