Inverse problem of identification of diffusion coefficient in convection-diffusion-reaction equation

Inverse extremum problem of identification of the diffusion coefficient in an elliptic equation of convection-diffusion-reaction is formulated. The solvability of this problem is proved, the application of Lagrange principle is justified and the optimality system is constructed for specific cost functional. The numerical algorithm based on Newton-method of nonlinear optimization and finite-element discretization of linear elliptic problems is developed and realized on computer. The results of numerical experiments are discussed.