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Background Results on Evolution Equations

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

Abstract

We recall some basic definitions and properties of functional analysis: unbounded dissipative operators, the Hille-Yosida semi-group generation theorem, local existence and uniqueness for semilinear problems, with applications to the heat equation and the wave equation in a bounded spatial domain. These preliminaries are useful to define the dynamical systems associated to semilinear PDE of parabolic or hyperbolic type.

References

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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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