Controllability of Partial Differential Equations Governed by Multiplicative Controls

  • Alexander Y. Khapalov

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
  7. Back Matter
    Pages 275-290

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

  • Alexander Y. Khapalov
    • 1
  1. 1., Department of MathematicsWashington State UniversityPullmanUSA

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