國立虎尾科技大學 |

The Convergence Problem for Dissipative Autonomous Systems = Classical Methods and Recent Advances /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The Convergence Problem for Dissipative Autonomous Systems/ by Alain Haraux, Mohamed Ali Jendoubi.
其他題名:	Classical Methods and Recent Advances /
作者:	Haraux, Alain.
其他作者:	Jendoubi, Mohamed Ali.
面頁冊數:	XII, 142 p. 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Dynamics. -
電子資源:	https://doi.org/10.1007/978-3-319-23407-6
ISBN:	9783319234076

The Convergence Problem for Dissipative Autonomous Systems = Classical 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. - 1st ed. 2015. - XII, 142 p. 1 illus. in color.online resource. - 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

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

592238
Dynamics.

LC Class. No.: QA313

Dewey Class. No.: 515.39

The Convergence Problem for Dissipative Autonomous Systems = Classical Methods and Recent Advances /
LDR:03125nam a22004095i 4500 001 967990
003 DE-He213
005 20200706112855.0
007 cr nn 008mamaa
008 201211s2015 gw | s |||| 0|eng d
020 $a 9783319234076 $9 978-3-319-23407-6
024 7 $a 10.1007/978-3-319-23407-6 $2 doi
035 $a 978-3-319-23407-6
050 4 $a QA313
072 7 $a PBWR $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBWR $2 thema
082 0 4 $a 515.39 $2 23
082 0 4 $a 515.48 $2 23
100 1 $a Haraux, Alain. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1069903
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.
250 $a 1st ed. 2015.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a XII, 142 p. 1 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 Dynamics. $3 592238
650 0 $a Ergodic theory. $3 672355
650 0 $a Partial differential equations. $3 1102982
650 0 $a Functional analysis. $3 527706
650 0 $a Operator theory. $3 527910
650 0 $a Differential equations. $3 527664
650 1 4 $a Dynamical Systems and Ergodic Theory. $3 671353
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Operator Theory. $3 672127
650 2 4 $a Ordinary Differential Equations. $3 670854
700 1 $a Jendoubi, Mohamed Ali. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1069904
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319234069
776 0 8 $i Printed edition: $z 9783319234083
830 0 $a SpringerBriefs in Mathematics, $x 2191-8198 $3 1255329
856 4 0 $u https://doi.org/10.1007/978-3-319-23407-6
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)