- Provides a survey of available techniques for stabilizing parabolic boundary value problems
- Draws from the author's years of lectures and teaching on control theory for parabolic equations
- Discusses the construction of nonlinear feedback controllers for steering system states
Buy this book
- About this book
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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.
- Table of contents (6 chapters)
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Preliminaries
Pages 1-26
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The Carleman Inequality for Linear Parabolic Equations
Pages 27-42
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Exact Controllability of Parabolic Equations
Pages 43-101
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Internal Controllability of Parabolic Equations with Inputs in Coefficients
Pages 103-127
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Feedback Stabilization of Semilinear Parabolic Equations
Pages 129-195
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Table of contents (6 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Controllability and Stabilization of Parabolic Equations
- Authors
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- VIOREL BARBU
- Series Title
- PNLDE Subseries in Control
- Series Volume
- 90
- Copyright
- 2018
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer International Publishing AG, part of Springer Nature
- eBook ISBN
- 978-3-319-76666-9
- DOI
- 10.1007/978-3-319-76666-9
- Hardcover ISBN
- 978-3-319-76665-2
- Softcover ISBN
- 978-3-030-09550-5
- Edition Number
- 1
- Number of Pages
- X, 226
- Topics
