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Controlabilite exacte, perturbations et stabilisation de systemes distribues

Lions, J.- L.



Controlabilite exacte, perturbations et stabilisation de systemes distribues

Tác giả: Lions, J.- L.
Loại tài liệu: Sách, chuyên khảo, tuyển tập
Ký hiệu: Lv6585
Mã giá: 93LI
Nội dung tóm tắt: Xem chi tiết
In Volume I of this book the author introduced the, by now well-known, Hilbert uniqueness method (H.U.M.) for the study of the exact controllability of distributed parameter systems. This method was applied to the wave equation, some models of plates and the elasticity system under various boundary conditions. H.U.M. may be systematically applied to all the reversible systems and provides an optimal control when the control acts either on the boundary or locally in the interior of the domain. In this second volume the author studies the exact controllability of perturbed distributed parameter systems. Various types of perturbations are considered but the main questions are as follows: first, the existence of a uniform time of exact controllability, i.e., which does not depend on the perturbations; and then, the continuous dependence of the controls with respect to the perturbations. The main problems addressed in this book are the following: (1) Coupled systems. (2) Exact controllability and penalization. (3) Exact controllability and singular perturbations. (4) Perturbations on the type of control applied to the system. (5) Perturbations of domains. (6) Homogenization. (7) System with memory terms. Many positive results are proven. Also, the R.H.U.M. (reverse Hilbert uniqueness method) is introduced for the study of reachability problems for nonreversible distributed parameter systems. The main techniques of optimal control theory and from partial differential equations used in this book are as follows: (a) H.U.M. and R.H.U.M. (b) Singular perturbation techniques. (c) Homogenization techniques. (d) Uniqueness and unique continuation results for partial differential equations. In several situations the author develops some formal calculations, whose rigorous justification is an open question. Each chapter of this book ends with a list of open problems. Reviewed by Enrique Zuazua
Mục lục: Xem chi tiết
Chapitre 1. Systemes couples Chapitre 2. Contrụlabilitộ exacte et penalisation Chapitre 3. Contrụlabilitộ exacte et perturbations singulieres Chapitre 5. Perturbations des modes d'action sur les systemes Chapitre 6. Perturbations des domaines Chapitre 7. Homogeneisation Chapitre 8. Systemes a memoire

Thông tin chi tiết

    Dạng tài liệu:Bản in
    Chỉ số ISBN:2-225-81474-0
    Ngôn ngữ:fre
    Mã giá:93LI
    Mã MSC:Đang cập nhật ...
    Tác giả:Lions, J.- L
    Nhan đề:Controlabilite exacte, perturbations et stabilisation de systemes distribues
    Xuất bản, phát hành:H : Paris , 1988
    Số trang:272;
    Kích thước:24 cm
    Bộ sách:Recherches en Mathộmatiques Appliquees, 9.

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  • ĐKCB: 9345020092163
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