(untitled) (International Journal of Mathematics and Physics, 2025)
The inverse problem for the advection-diffusion equation is considered in this paper. The study focuses on reconstructing a space-dependent source of a variable-coefficient advection-diffusion equation with separable sources from time-dependent temperature measurements at the right boundary of the domain. The Tikhonov regularization method is used to determine the space-dependent source function. These problems arise in various fields of science and engineering. The source term takes the form of separated variables, where one function describes the time evolution and the other represents the spatial distribution of some contaminant source. Such source terms also arise as control terms in the context of heat equations. Numerical experiments were conducted to demonstrate the accuracy and robustness of the proposed method. A non-iterative inversion algorithm is developed and numerically implemented for identifying the unknown space-dependent source. Consequently, identifying space-dependent or time-dependent sources is crucial in addressing environmental issues, which served as the motivation for proposing this problem. Key words: Inverse source problem, advection-diffusion equation, space-dependent heat source, Dirichlet data