Advertisement

Gradient-Like Systems

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

Abstract

The notion of gradient-like systems has been defined in several ways in the Literature. It refers basically to those systems for which pre compact trajectories converge to the set of equilibria. We give several equivalent definitions and show how to handle semi linear PDE of parabolic or hyperbolic type in this context.

References

  1. 1.
    H.B. Curry, The method of steepest descent for non-linear minimization problems. Quart. Appl. Math. 2, 258–261 (1944)MathSciNetzbMATHGoogle Scholar
  2. 2.
    J. Palis, W. de Melo, Geometric Theory of Dynamical Systems, ed. by A.K. Manning. An introduction. Translated from the Portuguese (Springer, New York, 1982)Google Scholar
  3. 3.
    A. Haraux, M. Kirane, Estimations \(C^1\) pour des problèmes paraboliques semi-linéaires. Ann. Fac. Sci. Toulouse Math. 5, 265–280 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    G.F. Webb, Compactness of bounded trajectories of dynamical systems in infinite-dimensional spaces. Proc. Roy. Soc. Edinburgh Sect. A 84, 19–33 (1979)MathSciNetCrossRefzbMATHGoogle Scholar

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

Personalised recommendations