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Controllability and Stabilization of Parabolic Equations

  • Viorel Barbu

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 90)

Also part of the PNLDE Subseries in Control book sub series (PNLDE-SC, volume 90)

Table of contents

  1. Front Matter
    Pages i-x
  2. Viorel Barbu
    Pages 1-26
  3. Back Matter
    Pages 219-226

About this book

Introduction

This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic equations, the author addresses the controllability of parabolic equations on a variety of domains and the spectral decomposition technique for representing them. This method is, in fact, designed for use in a wider class of parabolic systems that include the heat and diffusion equations. Later chapters develop another process that employs stabilizing feedback controllers with a finite number of unstable modes, with special attention given to its use in the boundary stabilization of Navier–Stokes equations for the motion of viscous fluid. In turn, these applied methods are used to explore related topics like the exact controllability of stochastic parabolic equations with linear multiplicative noise. 

Intended for graduate students and researchers working on control problems involving nonlinear differential equations, Controllability and Stabilization of Parabolic Equations is the distillation of years of lectures and research. With a minimum of preliminaries, the book leaps into its applications for control theory with both concrete examples and accessible solutions to problems in stabilization and controllability that are still areas of current research.  

Keywords

parabolic equations controllability and stabilization methods in control theory control engineering parabolic boundary values Carleman inequality Boundary stabilization of Navier–Stokes equations

Authors and affiliations

  • Viorel Barbu
    • 1
  1. 1.A1. I CUZA UNIVERSITYIASIRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-76666-9
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-76665-2
  • Online ISBN 978-3-319-76666-9
  • Series Print ISSN 1421-1750
  • Series Online ISSN 2374-0280
  • Buy this book on publisher's site
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