To the problem of rod heating

The construction of control boundary conditions is considered in the paper for the problem of heating a one-dimensional rod up to specified temperature. Two modifications of the method proposed by A. V. Fursikov are presented, these modifications allow us to take into account restrictions posed onto the structure of solution and the construl. Calculation results are presented for heating elements located both outside and inside of the rod. The obtained algorithms admit natural generalizations to a wide class of equations including nonlinear Navier–Stokes type equations and also problems of stabilization by initial data and the right-hand side.