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Boundary Stabilization of Parabolic Equations / by Ionuţ Munteanu
(PNLDE Subseries in Control. ISSN:27317374 ; 93)
版 | 1st ed. 2019. |
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出版者 | (Cham : Springer International Publishing : Imprint: Birkhäuser) |
出版年 | 2019 |
本文言語 | 英語 |
大きさ | XII, 214 p. 8 illus., 3 illus. in color : online resource |
著者標目 | *Munteanu, Ionuţ author SpringerLink (Online service) |
件 名 | LCSH:System theory LCSH:Control theory LCSH:Differential equations LCSH:Control engineering FREE:Systems Theory, Control FREE:Differential Equations FREE:Control and Systems Theory |
一般注記 | Preliminaries -- Stabilization of Abstract Parabolic Equations -- Stabilization of Periodic Flows in a Channel -- Stabilization of the Magnetohydrodynamics Equations in a Channel -- Stabilization of the Cahn-Hilliard System -- Stabilization of Equations with Delays -- Stabilization of Stochastic Equations -- Stabilization of Nonsteady States -- Internal Stabilization of Abstract Parabolic Systems This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this technique are wide ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard equations; and deterministic or stochastic semi-linear heat equations arising in biology, chemistry, and population dynamics modeling. The text provides answers to the following problems, which are of great practical importance: Designing the feedback law using a minimal set of eigenfunctions of the linear operator obtained from the linearized equation around the target state Designing observers for the considered control systems Constructing time-discrete controllers requiring only partial knowledge of the state After reviewing standard notations and results in functional analysis, linear algebra, probability theory and PDEs, the author describes his novel stabilization algorithm. He then demonstrates how this abstract model can be applied to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteady-states, and more. Boundary Stabilization of Parabolic Equations will be of particular interest to researchers in control theory and engineers whose work involves systems control. Familiarity with linear algebra, operator theory, functional analysis, partial differential equations, and stochastic partial differential equations is required HTTP:URL=https://doi.org/10.1007/978-3-030-11099-4 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783030110994 |
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EB00227651 |
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データ種別 | 電子ブック |
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分 類 | LCC:Q295 LCC:QA402.3-402.37 DC23:003 |
書誌ID | 4000120939 |
ISBN | 9783030110994 |
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※2017年9月4日以降