Titlebook: Optimal Control Problems for Partial Differential Equations on Reticulated Domains; Approximation and As Peter I. Kogut,Günter R. Leugering

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Introduction to the Asymptotic Analysis of Optimal Control Problems: A Parade of Examplesnce of .-periodic coefficients, .-periodically perforated zone of controls, quickly oscillating boundaries, etc.). In order to proceed with a mathematical description, we formulate the following parameterized OCP (OCP.), where . is a small parameter: . where

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Convergence of Sets in Variable Spacesasis of set convergence in fixed and varying spaces. In this context, we introduce different notions of limits for sequences of nonempty sets and give some applications to the theory of thin periodic and reticulated structures.

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Suboptimal Control of Linear Steady-State Processes on Thin Periodic Structures with Mixed Boundary →0. In view of this, it should be noted that the asymptotic analysis of boundary value problems in a perforated domain with small holes (without controls) has been intensively studied by many authors.

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Approximate Solutions of Optimal Control Problems for Ill-Posed Parabolic Problems on Thin Periodic ditions under which in the limit we do not obtain an optimal control problem (OCP), but rather some initial-boundary value problems with or without controls. Furthermore, we construct asymptotically suboptimal controls for the original problem and show an approximation property of such controls for small enough . near the optimal characteristics.

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Introduction,Es) on domains with a lattice-type structure. The investigation of optimal control problems for such structures is important to researchers working with cellular materials (lightweight materials) such as honeycomb structures, ceramic, metal, or polymeric foams which are used in automotive industry,

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