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Communications in Mathematical Physics

, Volume 256, Issue 3, pp 589–609 | Cite as

Existence of Self-Similar Solutions to Smoluchowski’s Coagulation Equation

  • Nicolas FournierEmail author
  • Philippe Laurençot
Article

Abstract

The existence of self-similar solutions to Smoluchowski’s coagulation equation has been conjectured for several years by physicists, and numerical simulations have confirmed the validity of this conjecture. Still, there was no existence result up to now, except for the constant and additive kernels for which explicit formulae are available. In this paper, the existence of self-similar solutions decaying rapidly at infinity is established for a wide class of homogeneous coagulation kernels.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Explicit Formula 
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 2005

Authors and Affiliations

  1. 1.Institut Elie Cartan – NancyUniversité Henri Poincaré – Nancy IVandoeuvre-lès-Nancy cedexFrance
  2. 2.Mathématiques pour l’Industrie et la Physique, CNRS UMR 5640Université Paul Sabatier – Toulouse 3Toulouse cedex 4France

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