Abstract: The optimal control of systems governed by linear elliptic partial differential equations has 

been fully investigated, however, there are relatively few numerical computations. As regards nonlinear 

systems both aspects of the subject appear to be equally neglected. In this study some of the results for 

optimal control of linear elliptic systems have been generalized to the nonlinear case. This was achieved 

by employing standard techniques of the nonlinear theory. After demonstrating the existence of the 

optimal controls, finite element methods were used to effect the discretization of the optimal control 

problem. The resulting finite dimensional problem was solved by a special approach. The theoretical 

investigations were completed by proving that approximate solutions reduce to exact solutions when the 

mesh size tends to zero. Finally an identification problem arising in biomedical engineering within the 

framework of functional anlysis was considered. This study was closed by a presentation and discussion 

of several related numerical results. 

Key words: Optimal control, nonlinear elliptic systems, numerical soliton and system identification.