國立虎尾科技大學 |

Controllability and stabilization of parabolic equations

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Controllability and stabilization of parabolic equations/ by Viorel Barbu.
Author:	Barbu, Viorel.
Published:	Cham :Springer International Publishing : : 2018.,
Description:	x, 226 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Control theory. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-76666-9
ISBN:	9783319766669

Controllability and stabilization of parabolic equations
Barbu, Viorel.

Controllability and stabilization of parabolic equations[electronic resource] /by Viorel Barbu. - Cham :Springer International Publishing :2018. - x, 226 p. :ill., digital ;24 cm. - Progress in nonlinear differential equations and their applications,v.901421-1750 ;. - Progress in nonlinear differential equations and their applications ;v.83..

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.

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.

ISBN: 9783319766669

Standard No.: 10.1007/978-3-319-76666-9doiSubjects--Topical Terms:

527674
Control theory.

LC Class. No.: QA402.3

Dewey Class. No.: 515.642

Controllability and stabilization of parabolic equations
LDR:02804nam a2200337 a 4500 001 925875
003 DE-He213
005 20180426112151.0
006 m d
007 cr nn 008maaau
008 190625s2018 gw s 0 eng d
020 $a 9783319766669 $q (electronic bk.)
020 $a 9783319766652 $q (paper)
024 7 $a 10.1007/978-3-319-76666-9 $2 doi
035 $a 978-3-319-76666-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA402.3
072 7 $a GPFC $2 bicssc
072 7 $a SCI064000 $2 bisacsh
072 7 $a TEC004000 $2 bisacsh
082 0 4 $a 515.642 $2 23
090 $a QA402.3 $b .B241 2018
100 1 $a Barbu, Viorel. $3 782973
245 1 0 $a Controllability and stabilization of parabolic equations $h [electronic resource] / $c by Viorel Barbu.
260 $a Cham : $c 2018. $b Springer International Publishing : $b Imprint: Birkhauser,
300 $a x, 226 p. : $b ill., digital ; $c 24 cm.
490 1 $a Progress in nonlinear differential equations and their applications, $x 1421-1750 ; $v v.90
505 0 $a 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.
520 $a 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.
650 0 $a Control theory. $3 527674
650 0 $a Parabolic operators. $3 1110662
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Systems Theory, Control. $3 669337
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Control. $3 782232
650 2 4 $a Engineering Mathematics. $3 1203947
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Progress in nonlinear differential equations and their applications ; $v v.83. $3 888907
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-76666-9
950 $a Mathematics and Statistics (Springer-11649)