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

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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.

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Authors and Affiliations

  1. Institut Elie Cartan – Nancy, Université Henri Poincaré – Nancy I, 239, 54506, Vandoeuvre-lès-Nancy cedex, France

    Nicolas Fournier

  2. Mathématiques pour l’Industrie et la Physique, CNRS UMR 5640, Université Paul Sabatier – Toulouse 3, 118 route de Narbonne, 31062, Toulouse cedex 4, France

    Philippe Laurençot

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  1. Nicolas Fournier
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  2. Philippe Laurençot
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Correspondence to Nicolas Fournier.

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Communicated by J.L. Lebowitz

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Fournier, N., Laurençot, P. Existence of Self-Similar Solutions to Smoluchowski’s Coagulation Equation. Commun. Math. Phys. 256, 589–609 (2005). https://doi.org/10.1007/s00220-004-1258-5

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  • DOI: https://doi.org/10.1007/s00220-004-1258-5

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