Iterative Processes in Optimization of Semilinear Hyperbolic Systems

Abstract The paper considers the problems of optimal control of multi-dimensional semilinear hyperbolic equations. The problems of such kind arise in modeling some phenomena of aero- and hydrodynamics, chemical technology, transfer processes. The necessary optimality condition is formulated as a pointwise maximum principle. The reasons for complex validation of the maximum principle at a transition from one-dimensional hyperbolic systems to multi-dimensional ones are explained. The maximum principle is used as a base for constructing a family of iterative methods, this being a final target of the work. The proposed methods are relaxation ones and converge at the maximum principle.