An inverse problem of identifying the time-dependent potential and source terms in a two-dimensional parabolic equation

In this article, simultaneous identification of the timewise lowest and source terms in a two-dimensional (2D) parabolic equation from knowledge additional measurements is studied. Existence uniqueness solution proved by means contraction mapping on small time interval. Since problem yet ill- posed (very errors time-average temperature input may cause large output potential functions), we need to regularize solution. Hence, regularization needed for retrieval unknown terms. The 2D computationally solved using ADE scheme reshaped as non-linear optimization Tikhonov function. This numerically studied MATLAB $lsqnonlin$ subroutine. Finally, present numerical example demonstrate accuracy efficiency proposed method. Our results show that an efficient unconditionally stable reconstructing coefficients minimal data which makes inverse (IP) unique.