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Titlebook: Domain Decomposition Methods in Optimal Control of Partial Differential Equations; John E. Lagnese,Günter Leugering Book 2004 Birkhäuser B

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书目名称Domain Decomposition Methods in Optimal Control of Partial Differential Equations
编辑John E. Lagnese,Günter Leugering
视频video
概述Emphasis is to put domain decomposition methods in the context of so-called virtual optimal control problems and, more importantly, to treat optimal control problems for partial differential equations
丛书名称International Series of Numerical Mathematics
图书封面Titlebook: Domain Decomposition Methods in Optimal Control of Partial Differential Equations;  John E. Lagnese,Günter Leugering Book 2004 Birkhäuser B
描述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-dimensional level. 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. A keyword in this context is parallelism. This development is perhaps best illustrated by the fact that we just encountered the 15th annual conference precisely on this topic. Without attempting to provide a complete list of introductory references let us just mention the monograph by Quarteroni and Valli [91] as a general up-to-date reference on domain decomposition methods for partial differential equations. The emphasis of this monograph is to put domain decomposition methods in the context of so-called virtual optimal control problems and, more importantly, to treat optimal control problems for partial differential equations and their decom­ position
出版日期Book 2004
关键词Optimal control; Partial differential equations; control; history; network; partial differential equation
版次1
doihttps://doi.org/10.1007/978-3-0348-7885-2
isbn_softcover978-3-0348-9610-8
isbn_ebook978-3-0348-7885-2Series ISSN 0373-3149 Series E-ISSN 2296-6072
issn_series 0373-3149
copyrightBirkhäuser Basel 2004
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Partial Differential Equations on Graphs, papers on this topic, but rather refer the reader to a recent proceedings volume [2] for an account of current research in this area. For higher-dimensional problems and, more importantly, for optimal control problems for partial differential equations on graphs or networked domains, see [61].
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https://doi.org/10.1007/978-3-031-42629-2ed and boundary controls. Next we consider optimal control problems for hyperbolic systems, in which final value control is emphasized. Higher-dimensional analogs of the methods and results obtained here are discussed in Chapters 6 to 9.
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Domain Decomposition for Elliptic Optimal Control Problems,rast to domain decomposition procedures as such, has attracted the attention of mathematicians only recently. We focus the discussion at the beginning on elliptic partial differential equations which, from a technical point of view, are the most accessible.
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Optimal Control of One-Dimensional Partial Differential Equations on Graphs, However, here we focus on partial differential equations on graphs and, more precisely, on elliptic and hyperbolic equations. We first discuss elliptic optimal control problems on graphs. The global problem is defined and domain decomposition procedures are formulated in the cases of both distribut
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