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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
63/2003

Dynamical scaling in Smoluchowski's coagulation equations: uniform convergence

Govind Menon and Robert L. Pego

Abstract

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 are simple and rely on the Fourier inversion formula and the solution by the method of characteristics for the Laplace transform.

Received:
Jul 11, 2003
Published:
Jul 11, 2003

Related publications

inJournal
2006 Repository Open Access
Govind Menon and Robert L. Pego

Dynamical scaling in Smoluchowski's coagulation equations : uniform convergence

In: SIAM review, 48 (2006) 4, pp. 745-768