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Domain Decomposition Methods in Optimal Control of Partial Differential Equations

This monograph considers problems of optimal control for partial differential equa­ tions of elliptic and, more importantly, of hyperbolic types on networked domains. The main goal is to describe, develop and analyze iterative space and time domain decompositions of such problems on the infinite-dim...

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Bibliographic Details
Main Authors: Lagnese, John E., Leugering, Günter (Author)
Format: eBook
Language:English
Published: Basel Birkhäuser 2004, 2004
Edition:1st ed. 2004
Series:International Series of Numerical Mathematics
Subjects:
Engineering
Calculus Of Variations And Optimization
Technology And Engineering
Mathematical Optimization
Calculus Of Variations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1 Introduction
  • 2 Background Material on Domain Decomposition
  • 2.1 Introduction
  • 2.2 Domain Decomposition for 1-d Problems
  • 2.3 Domain Decomposition Methods for Elliptic Problems
  • 3 Partial Differential Equations on Graphs
  • 3.1 Introduction
  • 3.2 Partial Differential Operators on Graphs
  • 3.3 Elliptic Problems on Graphs
  • 3.4 Hyperbolic Problems on Graphs
  • 4 Optimal Control of Elliptic Problems
  • 4.1 Introduction
  • 4.2 Distributed Controls
  • 4.3 Boundary Controls
  • 5 Control of Partial Differential Equations on Graphs
  • 5.1 Introduction
  • 5.2 Elliptic Problems
  • 5.3 Hyperbolic Problems
  • 6 Control of Dissipative Wave Equations
  • 6.1 Introduction
  • 6.2 Optimal Dissipative Boundary Control
  • 6.3 Time Domain Decomposition
  • 6.4 Decomposition of the Spatial Domain
  • 6.5 Space and Time Domain Decomposition
  • 7 Boundary Control of Maxwell’s System
  • 7.1 Introduction
  • 7.2 Optimal Dissipative Boundary Control
  • 7.3 Time Domain Decomposition
  • 7.4 Decomposition of the Spatial Domain
  • 7.5 Time and Space Domain Decomposition
  • 8 Control of Conservative Wave Equations
  • 8.1 Introduction
  • 8.2 Optimal Boundary Control
  • 8.3 Time Domain Decomposition
  • 8.4 Decomposition of the Spatial Domain
  • 8.5 The Exact Reachability Problem
  • 9 Domain Decomposition for 2-D Networks
  • 9.1 Elliptic Systems on 2-D Networks
  • 9.2 Optimal Control on 2-D Networks
  • 9.3 Decomposition of the Spatial Domain

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