Optimal Control of Nonsmooth Distributed Parameter Systems
The book is devoted to the study of distributed control problems governed by various nonsmooth state systems. The main questions investigated include: existence of optimal pairs, first order optimality conditions, state-constrained systems, approximation
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1459
Dan Tiba
Optimal Control of Nonsmooth Distributed Parameter Systems
Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona
Lecture Notes in Mathematics Edited by A. Oold, B. Eckmann and F. Takens
1459
Dan Tiba
Optimal Control of Nonsmooth Distributed Parameter Systems
Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona
Author
Dan Tiba Institute of Mathematics, Academy of Sciences Bdul Pacii 220, 79622 Bucharest, Romania
Mathematics Subject Classification (1980): 49-02, 49A29, 49B22, 49B15, 49B27,49D05 ISBN 3-540-53524-1 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-53524-1 Springer-Verlag New York Berlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1990 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210 - Printed on acid-free paper
INTRODUCTION
Starting with the pioneering work of Lions and Stam pacehia [73], much attention is paid in the literature to the investigation of nonlinear partial differential equations involving nondifferentiable and even discontinuous terms. This includes the case of variational inequalities and free boundary problems and the main motivation of their interest is given by the many models arising in such a form with an important area of applications. See the monographs of Kinderlehrer and Stampacchia [62], Friedman [47], Ockendon and Elliott [45] where a large number of examples from various domains are discussed. A natural direction of development of the theory is the study of related control problems and the first papers along these lines belong to Lions [71], Yvon [144], Mignot [74]. This may be also viewed as a continuation of the classical analysis of control systems governed by linear partial differential equations and we quote the wellknown book of Lions [68] in this respect. The present work may be inscribed as a contribution to the general effort of research in nonsmooth optimization problems associated with nonlinear partial differential equations. More precisely, the main aim of these notes is to examine distributed control problems governed by nonlinear evolution equations (parabolic or hyperbolic), in the absence of differentiability properties. In this setting, a special emphasis is given to nonlinear hyperbolic problems which are less discussed in the literature. In order to obtain a more complete image of the area of research we nave mentioned and to show other possible applications of the methods, several sections deal wi
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