The Convergence Problem for Dissipative Autonomous Systems : Classical Methods and Recent Advances / by Alain Haraux, Mohamed Ali Jendoubi
| データ種別 | 電子書籍 |
|---|---|
| 版 | 1st ed. 2015. |
| 出版者 | Cham : Springer International Publishing : Imprint: Springer |
| 出版年 | 2015 |
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| 書誌ID | OB01016566 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | 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. License restrictions may limit access Summary: 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 |
| 著者標目 | *Haraux, Alain Jendoubi, Mohamed Ali SpringerLink (Online service) |
| 統一書名標目 | SpringerBriefs in Mathematics, |
| 件 名 | LCSH:Mathematics LCSH:Dynamics LCSH:Ergodic theory LCSH:Functional analysis LCSH:Operator theory LCSH:Differential equations LCSH:Partial differential equations FREE:Mathematics FREE:Dynamical Systems and Ergodic Theory FREE:Partial Differential Equations FREE:Functional Analysis FREE:Operator Theory FREE:Ordinary Differential Equations |
| 分 類 | LCC:QA313 DC23:515.39 DC23:515.48 |
| 巻冊次 | ISBN:9783319234076 RefWorks出力（各巻） print ; ISBN:9783319234069 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
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