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49J52 Calculus of variations and optimal control; optimization -- Existence theories -- Nonsmooth analysis

49K20 Calculus of variations and optimal control; optimization -- Optimality conditions -- Problems involving partial differential equations

49-02 Calculus of variations and optimal control; optimization -- Research exposition (monographs, survey articles) En-ligne: Springerlink | Zentralblatt | MathSciNet

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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” (Zentralblatt)

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