| 书目名称 | The Convergence Problem for Dissipative Autonomous Systems |
| 副标题 | Classical Methods an |
| 编辑 | Alain Haraux,Mohamed Ali Jendoubi |
| 视频video | |
| 概述 | 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 i |
| 丛书名称 | SpringerBriefs in Mathematics |
| 图书封面 |  |
| 描述 | .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 ref |
| 出版日期 | Book 2015 |
| 关键词 | Dynamical systems; Gradient inequality; PDE; Stability of equilibria; Trend to equilibrium; partial diffe |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-23407-6 |
| isbn_softcover | 978-3-319-23406-9 |
| isbn_ebook | 978-3-319-23407-6Series ISSN 2191-8198 Series E-ISSN 2191-8201 |
| issn_series | 2191-8198 |
| copyright | The Author(s) 2015 |
发表于 2025-3-21 17:26:16
