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SpringerBriefs in Mathematics

The Convergence Problem for Dissipative Autonomous Systems

Classical Methods and Recent Advances

Authors: Haraux, Alain, Jendoubi, Mohamed Ali

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  • 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
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eBook $54.99
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  • ISBN 978-3-319-23407-6
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Softcover $69.99
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  • ISBN 978-3-319-23406-9
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  • Usually dispatched within 3 to 5 business days.
About this book

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.

Reviews

“The book … is ‘a snapshot of a hot or emerging topic’ and ‘a presentation of core concepts that students must understand in order to make independent contributions’. … it is a very pleasant and reader-friendly text with small surprises in different sections.” (Alp O. Eden, Mathematical Reviews, April, 2016)


Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-319-23407-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-319-23406-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Convergence Problem for Dissipative Autonomous Systems
Book Subtitle
Classical Methods and Recent Advances
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-23407-6
DOI
10.1007/978-3-319-23407-6
Softcover ISBN
978-3-319-23406-9
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XII, 142
Number of Illustrations
1 illustrations in colour
Topics