2003/06/24 by Govind Menon, Menon, Govind, Robert L. Pego +1
Computer Science · Environmental Science · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Advanced Mathematical Modeling in Engineering #Coagulation and Flocculation Studies #FOS: Physical sciences #Theoretical and Computational Physics #nlin.AO
paper · pdf · doi:10.48550/arxiv.nlin/0306048
Latex2e, 31 pages with 1 figure. Revised per referee's suggestions
openalex publication_date 2003/06/24 · arxiv created 2004/07/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski's coagulation equations for the solvable kernels K(x,y)=2, x+y and xy. We prove the uniform convergence of densities to the self-similar solution with exponential tails under the regularity hypothesis that a suitable moment have an integrable Fourier transform. For the discrete equations we prove uniform convergence under optimal moment hypotheses. Our results are completely analogous to classical local convergence theorems for the normal law in probability theory. The proofs rely on the Fourier inversion formula and the solution by the method of characteristics for the Laplace transform.