The Convergence Problem for Dissipative Au...

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

A rigorous and self-contained exposition of all the tools needed to develop the theory

A unified treatment of some results usually scattered in specialised research papers

A concrete approach to the important examples without ever sacrificing the beauty of the general theory behind them

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2015
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xii 142 S. 1 farbige Illustr. 142 p. 1 illus. in color.
ISBN-13:	9783319234069
ISBN-10:	3319234064
Sprache:	Englisch
Herstellernummer:	978-3-319-23406-9
Einband:	Kartoniert / Broschiert
Autor:	Jendoubi, Mohamed Ali Haraux, Alain
Auflage:	1st edition 2015
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 9 mm
Von/Mit:	Mohamed Ali Jendoubi (u. a.)
Erscheinungsdatum:	15.09.2015
Gewicht:	0,248 kg

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