Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena : International Conference in Vorau (Austria), July 18-24, 1993Wolfgang Desch, F. Kappel, Karl Kunisch |
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adjoint approximation assume assumptions beam boundary conditions boundary control bounded compact compactification consider constant constraints continuous convergence convex compactification defined denote differential equations Dirichlet boundary conditions distributed parameter systems domain dr dt dx dt dynamics energy estimate exists finite dimensional function Gâteaux differential given H¹(N heat equation Hence Hilbert space Imax inequality initial data integral k₁ L²(N Lemma linear operators Lipschitz Lipschitz continuous mapping Math Mathematics Subject Classification maximum principle measure method nonlinear norm obtain optimal control optimal control problem optimality conditions parabolic partial differential equations plate Pontryagin maximum principle Pontryagin's proof of Theorem Proposition result satisfies semigroup semilinear sequence SIAM space string structure T₁ Theorem 1.1 theory unique solution V₁ value problem vector w₁ zero ΣΤ Эт