Abstract: Firstly, we considered the identification problem of the dissipation coefficients for a class of degenerate elliptic equations. By treating the unknown dissipation coefficients as control functions, treating the solutions of the equation as state variables, and defining the objective  functional as the sum of the error between the state and the measurement values  and the artificial regularization term, we transformed the coefficient identification problem into an optimal control problem. Secondly,  the coefficient identification problem was studied  by using the research method of the optimal control problem. We gave the expression of the optimal control and proved the uniqueness of optimal control under appropriate conditions.

Key words: degenerate elliptic equation, coefficient identification, optimal control