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Some Basic Examples

  • Alain HarauxEmail author
  • Mohamed Ali Jendoubi
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

Before introducing sophisticated tools which allow to treat the most delicate cases, we list some simple model situations where convergence or non-convergence can be elucidated by elementary methods. For example all bounded trajectories of a finite dimensional convex gradient system are convergent, but a second order gradient-like system with dissipation having a continuum of equilibria may be divergent if the dissipation is quadratic or weaker for low velocities.

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis LionsSorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7598ParisFrance
  2. 2.Institut Préparatoire aux Etudes Scientifiques et TechniquesUniversité de CarthageLa MarsaTunisia
  3. 3.Faculté des sciences de Tunis, Laboratoire EDP-LR03ES04Université de Tunis El ManarTunisTunisia

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