Self-Similarity in a Coarsening Model in One Dimension
Motivated from asymptotic laws of motion for transition layers in the equation ut = ɛ 2uxx + u-u3, 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.
Proceedings of the Royal Society of London Series A
- Pub Date:
- March 1992