Abstract
Motivated from asymptotic laws of motion for transition layers in the equation
u
t
= Є
2
u
xx
+
u — u
2
, 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.
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