SelfSimilarity in a Coarsening Model in One Dimension
Abstract
Motivated from asymptotic laws of motion for transition layers in the equation u_{t} = ɛ ^{2}u_{xx} + uu^{3}, we consider the following model for coarsening of a fine partition of an interval: find the shortest subinterval of the partition, and joint it with its neighbours, combining three into one. Making a `random order assumption', we develop and study an unusual coagulation equation for the distribution of interval lengths. We establish the existence of a selfsimilar solution of this equation by using Laplace transform techniques. Simulation data indicate that random order does persist if present initially, and the distribution approaches similarity form.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 March 1992
 DOI:
 10.1098/rspa.1992.0035
 Bibcode:
 1992RSPSA.436..569C