Applied Optimal Control Theory of Distributed Systems : Springer : 9780306439933 : 030643993X : 28 Feb 1993 : Earlier investigations of optimal control problems utilized procedures that did not reveal important features of optimization problems for distributed parameter systems. This monograph explores the modern approach to optimization of distributed systems and reviews its applications, addressing selected issues of the optimal control of systems described by elliptic, hyperbolic, and parabolic equations. This volume is a substantially revised and updated version of K. A. Lurie's earlier work, Optimal Control in Problems of Mathematical Physics, published in Russian in 1975. The new text features discussions on the existence of optimal controls in the context of Pontryagin's maximum principle and examines the latest results obtained in the problem of the optimal design of nonhomogeneous bodies. Lurie utilizes the idea of composites in the problem of optimal conductivity distribution