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

• DOI: 10.1007/s00220-004-1258-5
• Publication Date: 2005-01-14T15:00:07Z
• Authors: Nicolas Fournier; Philippe Laurençot
• Keywords: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]; 45K05; large time behaviour; [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]; homogeneous coagulation kernels; Coalescence

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.