Identifying the coefficient of first-order in parabolic equation from final measurement data

This paper studies an inverse problem of recovering the first-order coefficient in parabolic equation when the final observation is given. Such problem has important application in a large field of applied science. The original problem is transformed into an optimal control problem by the optimization theory. The existence, uniqueness and necessary condition of the minimum for the control functional are established. By an elliptic bilateral variational inequality which is deduced from the necessary condition, an algorithm and some numerical experiments are proposed in the paper. The numerical results show that the proposed method is an accurate and stable method to determine the coefficient of first-order in the inverse parabolic problems.