Nonlinear inverse problems of time-harmonic wave suppression in regular waveguides

The paper deals with a theoretical and numerical study of nonlinear inverse problems of time-harmonic wave suppression in regular three-dimensional acoustic waveguides. In these problems the field, which is generated by a primary source is given and it is required to suppress it completely or to minimize it by the action of secondary sources. The problems are considered as the minimization problems of some cost functionals. The power radiated to the far zone of the waveguide or the potential energy of the field in some bounded domain of the waveguide are used as these functionals. The coordinates and amplitudes of the secondary antennas play the role of controls. Each of the mentioned functionals is a quadratic function of the complex intensity and, nonconvex general function of the point source coordinates. An efficient numerical method for solution of these problems is developed and some results of numerical experiments are discussed