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Mathematische Annalen

, Volume 321, Issue 1, pp 131–155 | Cite as

Asymptotically self-similar global solutions of a general semilinear heat equation

  • Seifeddine Snoussi
  • Slim Tayachi
  • Fred B. Weissler
Original article

Abstract.

We consider the general nonlinear heat equation \(\partial_t u = \Delta u +a|u|^{p_1-1}u+g(u), u(0)=\varphi,\) on \((0,\infty)\times I\!\!R^n ,\) where \(a\in I\!\!R, p_1>1+(2/n)\) and g satisfies certain growth conditions. We prove the existence of global solutions for small initial data with respect to a norm which is related to the structure of the equation. We also prove that some of those global solutions are asymptotic for large time to self-similar solutions of the single power nonlinear heat equation, i.e. with \(g\equiv 0.\)

Keywords

Growth Condition Initial Data Large Time Heat Equation Global Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Seifeddine Snoussi
    • 1
  • Slim Tayachi
    • 2
  • Fred B. Weissler
    • 3
  1. 1.Département de Mathématiques, Faculté des Sciences de Bizerte, Université Tunis II, Jarzouna 7021, Bizerte Tunisia (e-mail: seifeddine.snoussi@fsb.rnu.tn) TN
  2. 2.Département de Mathématiques, Faculté des Sciences de Tunis, Université Tunis II, Campus Universitaire, 1060 Tunis Tunisia (e-mail: slim.tayachi@fst.rnu.tn) TN
  3. 3.Laboratoire Analyse Géométrie et Applications, UMR CNRS 7539, Institut Galilée, Université Paris-Nord, 93430 Villetaneuse, France (e-mail: weissler@math.univ-paris13.fr) FR

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