Domain Decomposition Methods in Optimal Control of Partial Differential Equations [electronic resource] | Lagnese, John E, Leugering, Günter

Domain Decomposition Methods in Optimal Control of Partial Differential Equations
Author: John E. Lagnese, Günter Leugering
Published by Birkhäuser Basel
ISBN: 978-3-0348-9610-8
DOI: 10.1007/978-3-0348-7885-2

Table of Contents:

• Introduction
• Background Material on Domain Decomposition
• Partial Differential Equations on Graphs
• Domain Decomposition for Elliptic Optimal Control Problems
• Optimal Control of One-Dimensional Partial Differential Equations on Graphs
• Domain Decomposition in Optimal Final Value Control of Dissipative Wave Equations
• Domain Decomposition in Optimal Final Value Boundary Control of Maxwell’s System
• Optimal Final Value Boundary Control of Conservative Wave Equations
• Domain Decomposition for Distributed Parameter Systems on 2-D Networks

Preface -- 1. Introduction -- 2. Background Material on Domain Decomposition -- 3. Partial Differential Equations on Graphs -- 4. Optimal Control of Elliptic Problems -- 5. Control of Partial Differential Equations on Graphs -- 6. Control of Dissipative Wave Equations -- 7. Boundary Control of Maxwell's System -- 8. Control of Conservative Wave Equations -- 9. Domain Decomposition for 2D-Networks -- Bibliography -- Index
While domain decomposition methods have a long history dating back well over one hundred years, it is only during the last decade that they have become a major tool in numerical analysis of partial differential equations. This monograph considers problems of optimal control for partial differential equations 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 dimensional level