This book represents an extended and substantially revised version of my
earlierbook, Optimal Control in Problems ofMathematical Physics,
originally published in Russian in 1975. About 60% of the text has been
completely revised and major additions have been included which have
produced a practically new text. My aim was to modernize the
presentation but also to preserve the original results, some of which
are little known to a Western reader. The idea of composites, which is
the core of the modern theory of optimization, was initiated in the
early seventies. The reader will find here its implementation in the
problem of optimal conductivity distribution in an MHD-generatorchannel
flow.Sincethen it has emergedinto an extensive theory which is
undergoing a continuous development. The book does not pretend to be a
textbook, neither does it offer a systematic presentation of the theory.
Rather, it reflects a concept which I consider as fundamental in the
modern approach to optimization of dis- tributed systems.
Bibliographical notes, though extensive, do not pretend to be exhaustive
as well. My thanks are due to ProfessorJean-Louis Armand and
ProfessorWolf Stadler whose friendly assistance in translating and
polishing the text was so valuable. I am indebted to Mrs. Kathleen
Durand and Mrs. Colleen Lewis for the hard job of typing large portions
of the manuscript.