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Boundary Stabilization of Parabolic Equations

  • Ionuţ Munteanu

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 93)

Also part of the PNLDE Subseries in Control book sub series (PNLDE-SC, volume 93)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Ionuţ Munteanu
    Pages 1-17
  3. Ionuţ Munteanu
    Pages 19-48
  4. Ionuţ Munteanu
    Pages 49-76
  5. Ionuţ Munteanu
    Pages 93-107
  6. Ionuţ Munteanu
    Pages 109-126
  7. Ionuţ Munteanu
    Pages 127-169
  8. Ionuţ Munteanu
    Pages 171-185
  9. Back Matter
    Pages 207-214

About this book

Introduction

This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this technique are wide ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard equations; and deterministic or stochastic semi-linear heat equations arising in biology, chemistry, and population dynamics modeling.

The text provides answers to the following problems, which are of great practical importance:
  • Designing the feedback law using a minimal set of eigenfunctions of the linear operator obtained from the linearized equation around the target state
  • Designing observers for the considered control systems
  • Constructing time-discrete controllers requiring only partial knowledge of the state
After reviewing standard notations and results in functional analysis, linear algebra, probability theory and PDEs, the author describes his novel stabilization algorithm. He then demonstrates how this abstract model can be applied to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteady-states, and more.
 
Boundary Stabilization of Parabolic Equations will be of particular interest to researchers in control theory and engineers whose work involves systems control. Familiarity with linear algebra, operator theory, functional analysis, partial differential equations, and stochastic partial differential equations is required.

Keywords

Parabolic Partial Differential Equations Boundary Stabilization Magnetohydrodynamics equations Cahn-Hilliard System Stochastic Partial Differential Equations Feedback control Control theory

Authors and affiliations

  • Ionuţ Munteanu
    • 1
  1. 1.Faculty of MathematicsAlexandru Ioan Cuza UniversityIaşiRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-11099-4
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-11098-7
  • Online ISBN 978-3-030-11099-4
  • Series Print ISSN 1421-1750
  • Series Online ISSN 2374-0280
  • Buy this book on publisher's site
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