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Optimal control of nonsmooth distributed parameter systems. (English) Zbl 0732.49002
Lecture Notes in Mathematics, 1459. Berlin etc.: Springer-Verlag. vi, 159 p. DM 30.00 (1990).
This monograph discusses a variety of optimal control problems governed by partial differential equations. The main theme is to consider problems which are amenable to study via the theory of nonlinear semigroups and monotone operators, e.g. semilinear wave equations, parabolic equations arising from monotone heat flux, obstacle problems, free boundary problems. With each class of problems the author proves existence of an optimal control and then derives necessary conditions fulfilled by the optimal control. In addition the book presents a short introduction on the elements of nonlinear analysis used in the later chapters. The book is well written and provides a nice supplement to the classic study of J.-L. Lions, “Optimal control of systems governed by partial differential equations” (New York 1971; for a review of the 1968 French original see Zbl 0179.418).

MSC:
49-02 Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control
49J20 Existence theories for optimal control problems involving partial differential equations
49J52 Nonsmooth analysis
49K20 Optimality conditions for problems involving partial differential equations
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