SIMULTANEOUS RECONSTRUCTION OF DUAL TIME-DEPENDENT COEFFICIENTS IN COUPLED TIME-FRACTIONAL DIFFUSION SYSTEMS
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Date
2026
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Abstract
This dissertation is devoted to the study of an inverse source problem for a coupled system
of time-fractional parabolic equations. The main objective is to simultaneously identify two
unknown time-dependent source terms from additional measurement data.
The work is organized into two parts. First, the associated direct problem is investigated,
anda numerical approximation is developed using a Legendre–Galerkin spectral method. This
discretization provides accurate approximations of the state variables and serves as the basis
for the inverse analysis.
The second part focuses on the inverse problem. A non-iterative numerical reconstruction
procedure is proposed for recovering the unknown sources from integral measurement data.
The method is based on explicit identification formulas for the source terms, combined with
the numerical approximation of the direct problem.