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


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 \(g\equiv 0.\)


Growth Condition Initial Data Large Time Heat Equation Global Solution 


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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: TN
  2. 2.Département de Mathématiques, Faculté des Sciences de Tunis, Université Tunis II, Campus Universitaire, 1060 Tunis Tunisia (e-mail: TN
  3. 3.Laboratoire Analyse Géométrie et Applications, UMR CNRS 7539, Institut Galilée, Université Paris-Nord, 93430 Villetaneuse, France (e-mail: FR

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