Determination of an unknown source term temperature distribution for the sub-diffusion equation at the initial and final data
Date
2017-10-11
Authors
Kirane, Mokhtar
Samet, Bessem
Torebek, Berikbol T.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Inverse problem, Involution, Nonlocal sub-diffusion equation, Fractional-time diffusion equation
Citation
Kirane, M., Samet, B., & Torebek, B. T. (2017). Determination of an unknown source term temperature distribution for the sub-diffusion equation at the initial and final data. <i>Electronic Journal of Differential Equations, 2017</i>(257), pp. 1-13.