© 2010

Controllability of Partial Differential Equations Governed by Multiplicative Controls


  • 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 Lecture Notes in Mathematics book series (LNM, volume 1995)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Alexander Y. Khapalov
    Pages 1-12
  3. Multiplicative Controllability of Parabolic Equations

  4. Multiplicative Controllability of Hyperbolic Equations

  5. Controllability for Swimming Phenomenon

    1. Front Matter
      Pages 158-158
    2. Alexander Y. Khapalov
      Pages 159-164
    3. Alexander Y. Khapalov
      Pages 165-170
    4. Alexander Y. Khapalov
      Pages 171-193
    5. Alexander Y. Khapalov
      Pages 219-236
    6. Alexander Y. Khapalov
      Pages 237-262
  6. Multiplicative Controllability Properties of the Schrödinger Equation

    1. Front Matter
      Pages 264-264

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.


Mathematica differential equation hyperbolic equation modeling partial differential equation

Authors and affiliations

  1. 1., Department of MathematicsWashington State UniversityPullmanUSA

Bibliographic information

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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)