Controllability and Stabilization of Parabolic Equations

Viorel Barbu (Autor)

Buch | Hardcover

X, 226 Seiten

2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-76665-2 (ISBN)

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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.

Preface.- Acronyms.- Preliminaries.- The Carleman Inequality for Linear Parabolic Equations.- Exact Controllability of Parabolic Equations.- Internal Controllability of Parabolic Equations with Inputs in Coefficients.- Feedback Stabilization of Semilinear Parabolic Equations.- Boundary Stabilization of Navier-Stokes Equations.- Index.

"Several well-chosen examples of illustration are derived with (mostly) practical interpretations, which increases the clarity of the presentation. Also, various comments are given at the end of each chapter which extend the discussion of different results of this book and related classical works from the literature." (Mohamed Ouzahra, SIAM Review, Vol. 63 (4), December, 2021)

“Several well-chosen examples of illustration are derived with (mostly) practical interpretations, which increases the clarity of the presentation. Also, various comments are given at the end of each chapter which extend the discussion of different results of this book and related classical works from the literature.” (Mohamed Ouzahra, SIAM Review, Vol. 63 (4), December, 2021)

Erscheinungsdatum	17.05.2018
Reihe/Serie	PNLDE Subseries in Control
Reihe/Serie	Progress in Nonlinear Differential Equations and Their Applications
Zusatzinfo	X, 226 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	520 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Boundary stabilization of Navier-Stokes equations • Boundary stabilization of Navier–Stokes equations • Carleman inequality • control engineering • controllability and stabilization methods in contr • controllability and stabilization methods in control theory • parabolic boundary values • Parabolic equations • Partial differential equations
ISBN-10	3-319-76665-1 / 3319766651
ISBN-13	978-3-319-76665-2 / 9783319766652
Zustand	Neuware