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Journal of Evolution Equations

, Volume 8, Issue 4, pp 727–748 | Cite as

Non-global existence for an Allen-Cahn-Gurtin equation with logarithmic free energy

  • Laurence CherfilsEmail author
  • Morgan Pierre
Article

Abstract.

We consider a simple Allen-Cahn-Gurtin model with a logarithmic potential. We show that strong solutions exist locally in time, but not globally in general. This is due to a lack of maximum principle.

Keywords:

Maximum principle nonlinear pseudoparabolic equation 

Mathematics Subject Classifications (2000):

35K70 35B50 

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Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Laboratoire MIAUniversité de La RochelleLa Rochelle Cedex 1France
  2. 2.Laboratoire de Mathématiques UMR CNRS 6086Université de PoitiersFuturoscope ChasseneuilFrance

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