Abstract In this paper, we consider heat and mass transfer in a rectangular multilayer body, where solutions of the 2D equations are connected by internal interface conditions. Similar problems were solved for 1D multilayer body. Here, we focus on an inverse problem (IP) to determine the left and right boundary conditions from integral measured output on the last or the first layer, respectively. In the case of unknown left boundary condition, we begin by reducing the 2D heat problem into 1D problem. This reduction allows us to formulate new 1D IPs within each layer to identify the solution and external left Dirichlet boundary condition. We solve these problems sequentially, moving from the last layer to the first. At the last layer, using the right boundary condition and the integral observation, we find the solution and left Dirichlet and Neumann boundary conditions. Next, from interface conditions, we obtain Dirichlet and Neumann right boundary condition of the preceding layer and solve the IP for identifying its left boundary condition. Following this approach, we advance to the first layer, where we similarly determine the left Dirichlet boundary condition. Well‐posedness both for direct (forward) and IPs is shown. For the numerical solution of the direct and IPs, we construct finite difference schemes. Tikhonov regularization is used for the computation of IPs. Results from computational simulations are presented and discussed.
Koleva et al. (Thu,) studied this question.