Functional and numerical solution of a control problem originating from heat transfer

The solution of a nonlinear parabolic equation is studied from both the functional and the numerical points of view. Existence, uniqueness, and stability results are given. A boundary-control problem is then presented. Expressions of the gradient and the Hessian of the cost function are given with some details, and the Newton method is compared with a gradient method and the Fletcher-Reeves method. Numerical results are given. The paper concludes with a discussion of the advantages of the Newton method as applied to a control problem.