ADJOINT METHOD OF PARAMETER IDENTIFICATION FOR SOME NON-LINEAR REACTION-DIFFUSION SYSTEMS

This paper deals with the problem of determining two unknown parameters of some nonlinear reaction-diffusion models. These reaction-diffusion models are derived from applications in the groundwater flow transport, environmental sciences, gas dynamics, heat and mass transfer, industrial automatization and some other engineering technological fields. The adjoint method based on the variational principle is a relatively new optimal control method. It is used in the identification of the unknown diffusion coefficient, and some coefficients of the nonlinear sink or source terms in these systems. At first, the problem is transferred into an optimization problem of minimizing a functional, and the adjoint equations of the governing equations are derived from the adjoint method. Then, the formulas are given to calculate the gradient of the objective function with respect to the couple of unknown parameters. At last, an iterative gradient-based optimization algorithm is presented for solving the optimization problem. A numerical example is offered in the end. It shows the effectiveness of the proposed approach.