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Asymptotically self-similar global solutions of a general semilinear heat equation |
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| Authors: | Seifeddine Snoussi Slim Tayachi Fred B Weissler |
| Institution: | (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) 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) Laboratoire Analyse Géométrie et Applications, UMR CNRS 7539, Institut Galilée, Université Paris-Nord, 93430 Villetaneuse, France (e-mail: weissler@math.univ-paris13.fr) , FR |
| Abstract: | We consider the general nonlinear heat equation on where 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 Received: 23 July 1999 / Accepted: 14 December 2000 / Published online: 23 July 2001 |
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