Self-similarity in a coarsening model in one dimension
Jack Carr, Robert L. Pego · Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences · 1992
Abstract Motivated from asymptotic laws of motion for transition layers in the equation ut = Є2uxx + u — u2, 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 self-similar 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.