The Scaling Attractor and Ultimate Dynamics for Smoluchowski's Coagulation Equations

We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels K(x, y) = 2, x + y and xy. In another work, we classified all self-similar solutions and all universality classes (domains of attraction) for scaling limits under weak convergence (Comm. Pure Appl. Math 57 (2004)1197-1232). Here we add to this a complete description of the set of all limit points of solutions modulo scaling (the scaling attractor) and the dynamics on this limit set (the ultimate dynamics). The main tool is Bertoin's L

• Type: Journal
• Year: 2008
• Where: JNS
• Authors: Govind Menon, Robert L. Pego
• Keywords: Dynamic Scaling, JNS 2008, Modulo Scaling, Simplest Rate Kernels