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hal-00364722, version 1

Summability of solutions of the heat equation with inhomogeneous thermal conductivity in two variables

Werner Balser () 1, Michèle Loday-Richaud (Author to contact preferably) 2

Advances in Dynamical Systems and Applications 4, 2 (2009) 159-177

Abstract: We investigate Gevrey order and 1-summability properties of the formal solution of a general heat equation in two variables. In particular, we give necessary and sufficient conditions for the 1-summability of the solution in a given direction. When restricted to the case of constants coefficients, these conditions coincide with those given by D.A. Lutz, M. Miyake, R. Schaefke in a 1999 article, and we thus provide a new proof of their result.

  • 1:  Abteilung Angewandte Analysis Universitat Ulm
  • Universitat Ulm
  • 2:  Laboratoire Angevin de REcherche en MAthématiques (LAREMA)
  • CNRS : UMR6093 – Université d'Angers
  • Collaboration : Werner BALSER; Michèle LODAY-RICHAUD
  • Domain : Mathematics/Dynamical Systems
    Mathematics/Analysis of PDEs
  • Keywords : heat equation – Gevrey series – 1-summability
  • Internal note : BalserLoday
  • Comment : 16 pages
 
  • hal-00364722, version 1
  • http://hal.archives-ouvertes.fr/hal-00364722
  • oai:hal.archives-ouvertes.fr:hal-00364722
  • From: Michèle Loday-Richaud <>
  • Submitted on: Thursday, 26 February 2009 20:39:55
  • Updated on: Sunday, 13 June 2010 19:56:14