Asymptotic behavior of solutions to multiplicative control problems for elliptic equations

The problems of optimal multiplicative control for the Helmholtz equation and the diffusion equation are studied. The control function is included multiplicatively in a mixed-type boundary condition specified on the entire domain boundary or its part. For each of the models under study, an iterative method for determining an approximate solution is constructed and theoretically substantiated for sufficiently large values of the regularization parameter.