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The Infinite Dimensional Case

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

Abstract

This second core chapter concerns the convergence problem in infinite dimensions. In this framework, analyticity of the potential no longer implies the Łojasiewicz gradient inequality. We devise an essentially optimal condition for this inequality to hold. Applications to semi linear PDE of parabolic or hyperbolic type are given as an application of general theorems.

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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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