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Optimization in Elliptic Problems with Applications to Mechanics of Deformable Bodies and Fluid Mechanics

  • Book
  • © 2000

Overview

Authors:
  1. William G. Litvinov

    1. Institute of Statics and Dynamics of Aero-Space Structures, University of Stuttgart, Stuttgart, Deutschland

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Part of the book series: Operator Theory: Advances and Applications (OT, volume 119)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxii
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  2. Basic Definitions and Auxiliary Statements

    • William G. Litvinov
    Pages 1-79

  3. Optimal Control by Coefficients in Elliptic Systems

    • William G. Litvinov
    Pages 81-176

  4. Control by the Right-hand Sides in Elliptic Problems

    • William G. Litvinov
    Pages 177-208

  5. Direct Problems for Plates and Shells

    • William G. Litvinov
    Pages 209-286

  6. Optimization of Deformable Solids

    • William G. Litvinov
    Pages 287-429

  7. Optimization Problems for Steady Flows of Viscous and Nonlinear Viscous Fluids

    • William G. Litvinov
    Pages 431-501

  8. Back Matter

    Pages 503-522
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Keywords

About this book

This book is intended to be both a thorough introduction to contemporary research in optimization theory for elliptic systems with its numerous applications and a textbook at the undergraduate and graduate level for courses in pure or applied mathematics or in continuum mechanics. Various processes of modern technology and production are described by el­ liptic partial differential equations. Optimization of these processes reduces to op­ timization problems for elliptic systems. The numerical solution of such problems is associated with the solution of the following questions. 1. The setting of the optimization problem ensuring the existence of a solution on a set of admissible controls, which is a subset of some infinite-dimensional vector space. 2. Reduction of the infinite-dimensional optimization problem to a sequence of finite-dimensional problems such that the solutions of the finite-dimensional problems converge, in a sense, to the solution of the infinite-dimensional problem.3. Numerical solution of the finite-dimensional problems.

Reviews

“The monograph is written in an accessible and self-contained manner. It would be of a great interest to researchers working in optimization theory for partial differential equations and its applications as well as for graduate students with interests in applications of the theory of optimal control to real problems from mechanics.” (U.Raitums, zbMATH 0947.49001, 2022)

Authors and Affiliations

  • Institute of Statics and Dynamics of Aero-Space Structures, University of Stuttgart, Stuttgart, Deutschland

    William G. Litvinov

Bibliographic Information

  • Book Title: Optimization in Elliptic Problems with Applications to Mechanics of Deformable Bodies and Fluid Mechanics

  • Authors: William G. Litvinov

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8387-0

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2000

  • Hardcover ISBN: 978-3-7643-6199-0Published: 01 April 2000

  • Softcover ISBN: 978-3-0348-9545-3Published: 31 October 2012

  • eBook ISBN: 978-3-0348-8387-0Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XXII, 522

  • Topics: Engineering Fluid Dynamics, Analysis

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