國立高雄大學圖資館 |

Language: English

Back

The convergence problem for dissipat...

Haraux, Alain.

The convergence problem for dissipative autonomous systemsclassical methods and recent advances /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The convergence problem for dissipative autonomous systemsby Alain Haraux, Mohamed Ali Jendoubi.
Reminder of title:	classical methods and recent advances /
Author:	Haraux, Alain.
other author:	Jendoubi, Mohamed Ali.
Published:	Cham :Springer International Publishing :2015.
Description:	xii, 142 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Convergence.
Online resource:	http://dx.doi.org/10.1007/978-3-319-23407-6
ISBN:	9783319234076$q(electronic bk.)

The convergence problem for dissipative autonomous systemsclassical methods and recent advances /
Haraux, Alain.

The convergence problem for dissipative autonomous systemsclassical methods and recent advances /[electronic resource] :by Alain Haraux, Mohamed Ali Jendoubi. - Cham :Springer International Publishing :2015. - xii, 142 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

1 Introduction -- 2 Some basic tools -- 3 Background results on Evolution Equations -- 4 Uniformly damped linear semi-groups -- 5 Generalities on dynamical systems -- 6 The linearization method -- 7 Gradient-like systems -- 8 Liapunov's second method - invariance principle -- 9 Some basic examples -- 10 The convergence problem in finite dimensions -- 11 The infinite dimensional case -- 12 Variants and additional results.

The book investigates classical and more recent methods of study for the asymptotic behavior of dissipative continuous dynamical systems with applications to ordinary and partial differential equations, the main question being convergence (or not) of the solutions to an equilibrium. After reviewing the basic concepts of topological dynamics and the definition of gradient-like systems on a metric space, the authors present a comprehensive exposition of stability theory relying on the so-called linearization method. For the convergence problem itself, when the set of equilibria is infinite, the only general results that do not require very special features of the non-linearities are presently consequences of a gradient inequality discovered by S. Lojasiewicz. The application of this inequality jointly with the so-called Liapunov-Schmidt reduction requires a rigorous exposition of Semi-Fredholm operator theory and the theory of real analytic maps on infinite dimensional Banach spaces, which cannot be found anywhere in a readily applicable form. The applications covered in this short text are the simplest, but more complicated cases are mentioned in the final chapter, together with references to the corresponding specialized papers.

ISBN: 9783319234076$q(electronic bk.)

Standard No.: 10.1007/978-3-319-23407-6doiSubjects--Topical Terms:

182684
Convergence.

LC Class. No.: QA295

Dewey Class. No.: 515.24

The convergence problem for dissipative autonomous systemsclassical methods and recent advances /
LDR:02727nmm a2200325 a 4500 001 476967
003 DE-He213
005 20160414165556.0
006 m d
007 cr nn 008maaau
008 160526s2015 gw s 0 eng d
020 $a 9783319234076$q(electronic bk.)
020 $a 9783319234069$q(paper)
024 7 $a 10.1007/978-3-319-23407-6 $2 doi
035 $a 978-3-319-23407-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA295
072 7 $a PBWR $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 515.24 $2 23
090 $a QA295 $b .H254 2015
100 1 $a Haraux, Alain. $3 731775
245 1 4 $a The convergence problem for dissipative autonomous systems $h [electronic resource] : $b classical methods and recent advances / $c by Alain Haraux, Mohamed Ali Jendoubi.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xii, 142 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8198
505 0 $a 1 Introduction -- 2 Some basic tools -- 3 Background results on Evolution Equations -- 4 Uniformly damped linear semi-groups -- 5 Generalities on dynamical systems -- 6 The linearization method -- 7 Gradient-like systems -- 8 Liapunov's second method - invariance principle -- 9 Some basic examples -- 10 The convergence problem in finite dimensions -- 11 The infinite dimensional case -- 12 Variants and additional results.
520 $a The book investigates classical and more recent methods of study for the asymptotic behavior of dissipative continuous dynamical systems with applications to ordinary and partial differential equations, the main question being convergence (or not) of the solutions to an equilibrium. After reviewing the basic concepts of topological dynamics and the definition of gradient-like systems on a metric space, the authors present a comprehensive exposition of stability theory relying on the so-called linearization method. For the convergence problem itself, when the set of equilibria is infinite, the only general results that do not require very special features of the non-linearities are presently consequences of a gradient inequality discovered by S. Lojasiewicz. The application of this inequality jointly with the so-called Liapunov-Schmidt reduction requires a rigorous exposition of Semi-Fredholm operator theory and the theory of real analytic maps on infinite dimensional Banach spaces, which cannot be found anywhere in a readily applicable form. The applications covered in this short text are the simplest, but more complicated cases are mentioned in the final chapter, together with references to the corresponding specialized papers.
650 0 $a Convergence. $3 182684
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 273794
650 2 4 $a Partial Differential Equations. $3 274075
650 2 4 $a Functional Analysis. $3 274845
650 2 4 $a Operator Theory. $3 274795
650 2 4 $a Ordinary Differential Equations. $3 273778
700 1 $a Jendoubi, Mohamed Ali. $3 731776
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in mathematics. $3 558795
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-23407-6
950 $a Mathematics and Statistics (Springer-11649)