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

  • William G. Litvinov

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

Table of contents

  1. Front Matter
    Pages i-xxii
  2. William G. Litvinov
    Pages 1-79
  3. William G. Litvinov
    Pages 81-176
  4. William G. Litvinov
    Pages 177-208
  5. William G. Litvinov
    Pages 209-286
  6. William G. Litvinov
    Pages 287-429
  7. Back Matter
    Pages 503-522

About this book

Introduction

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.

Keywords

Boundary value problem Hilbert space Operator Sobolev space Transformation electromagnetic wave fluid mechanics functional analysis mechanics model operator theory optimization partial differential equation statics

Authors and affiliations

  • William G. Litvinov
    • 1
  1. 1.Institute of Statics and Dynamics of Aero-Space StructuresUniversity of StuttgartStuttgartDeutschland

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