Original Papers

Zeitschrift für angewandte Mathematik und Physik ZAMP

, Volume 43, Issue 1, pp 63-124

First online:

Convergence in gradient-like systems with applications to PDE

  • Jack K. HaleAffiliated withCenter for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology
  • , Geneviève RaugelAffiliated withLab. d'Analyse Numérique, CNRS et Université de Paris-Sud

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In gradient-like systems, the limit set of an orbit belongs to the set of equilibrium points. We give easily applied conditions to determine when this limit set is a single point. Applications are given to parabolic equations, linearly damped hyperbolic equations as well as their discretizations.