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Controllability of Partial Differential Equations Governed by Multiplicative Controls

  • Book
  • © 2010

Overview

Authors:
  1. Alexander Y. Khapalov

    1. , Department of Mathematics, Washington State University, Pullman, USA

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  • Physically motivated, mathematically challenging and timely
  • Relatively few results are available in the field
  • The results described in this book are certainly novel and original

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1995)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introduction

    • Alexander Y. Khapalov
    Pages 1-12

  5. Controllability for Swimming Phenomenon

    1. Front Matter

      Pages 158-158
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    2. Introduction

      • Alexander Y. Khapalov
      Pages 159-164

    3. A “Basic” 2-D Swimming Model

      • Alexander Y. Khapalov
      Pages 165-170

    4. The Well-Posedness of a 2-D Swimming Model

      • Alexander Y. Khapalov
      Pages 171-193

    5. Geometric Aspects of Controllability for a Swimming Phenomenon

      • Alexander Y. Khapalov
      Pages 195-217

    6. Local Controllability for a Swimming Model

      • Alexander Y. Khapalov
      Pages 219-236

    7. Global Controllability for a “Rowing” Swimming Model

      • Alexander Y. Khapalov
      Pages 237-262

  6. Multiplicative Controllability Properties of the Schrödinger Equation

    1. Front Matter

      Pages 264-264
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Keywords

About this book

The goal of this monograph is to address the issue of the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The mathematical models we examine include the linear and nonlinear parabolic and hyperbolic PDE's, the Schrödinger equation, and coupled hybrid nonlinear distributed parameter systems modeling the swimming phenomenon. The book offers a new, high-quality and intrinsically nonlinear methodology to approach the aforementioned highly nonlinear controllability problems.

Reviews

From the reviews:

“This book offers a detailed study of controllability of infinite-dimensional control systems described by partial differential equations (PDEs), for which the control input appears in a multiplicative way in the differential equations. The book has features that are not often encountered simultaneously in the rest of the literature … . the book is interesting and will have an impact on the topic of the controllability of infinite-dimensional systems. Rigorous proofs are provided for all the results contained in the book.” (Iasson Karafyllis, Mathematical Reviews, Issue 2011 h)

“In this book, the control of evolution processes governed by partial differential equations is studied. … The book is well-written and a welcome addition to the bookshelf for mathematicians with interest in control theory and also researchers in control engineering.” (Martin Gugat, Zentralblatt MATH, Vol. 1210, 2011)

Authors and Affiliations

  • , Department of Mathematics, Washington State University, Pullman, USA

    Alexander Y. Khapalov

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