Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations
 フォーマット:
 電子ブック
 責任表示:
 by Alexander Y. Khapalov
 本文言語:
 英語
 出版情報:
 Cham, Germany. 2017. Springer International Publishing,Imprint: Springer
 概要:
 This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time. Based on the author’s extensive research in the area of controllability theory, this monograph specifically focuses on the issues of controllability, observability, and stabilizability for parabolic and hyperbolic partial differential equations. The topics in this book also cover related applied questions such as the problem of localization of unknown pollution sources based on information obtained from point sensors that arise in environmental monitoring. Researchers and graduate students interested in controllability theory of partial differential equations and its applications will find this book to be an invaluable resource to their studies. … 続きを見る
 目次:

1. Introduction Part I: 2. Continuous observability of the heat equation under a single mobile point sensor 3. Continuous observability of the 2nd order paragolic equations under degenerate mobile sensors Part II: 4. Behavior of solutions of the semilinear heat equation in vanishing time and controllability 5. Controllability of the semiliniear heat equation with sublinear term and degenerate actuator 6. Controllability of the semilinear reactiondiffusion equation with degenerate actuator 7. Semilinear parabolic equations: Mobile point controls vs the locally distributed ones Part III: 8. Degenerate sensors in source localization and sensor placement problems Part IV: 9. Continuous observability of hyperbolic equations under degenerate sensors 10. Controllability of the wave equation governed by mobile point controls Part V: 11. Exponential decay for the wave equation equipped with a point damping device 12. A vibrating string with shuttlelike point dampers and related observability properties References. . 1. Introduction Part I: 2. Continuous observability of the heat equation under a single mobile point sensor 3. Continuous observability of the 2nd order paragolic equations under degenerate mobile sensors Part II: 4. Behavior of solutions of the semilinear heat equation in vanishing time and controllability 5. Controllability of the semiliniear heat equation with sublinear term and degenerate actuator 6. Controllability of the semilinear reactiondiffusion equation with degenerate actuator
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