1:00 pm Wednesday, March 21, 2012
Analysis Seminar: Self-similarity for a generalized Smoluchowski equation by Nicholas Leger (Carnegie Mellon) in RLM 10.176
We investigate the existence, uniqueness, and long-time behavior of solutions to a new coagulation model arising in the theory of branching processes. Informally, the equation models a coalescence process with multiple interactions, where the size and number of interacting clusters are sampled randomly. It is well-known that solutions of the equation correspond to L\'{e}vy measures for an associated continuous-state branching process, and we give an existence proof independent of the latter theory. Also, under a suitable regular variation assumption on the sampling measure, we characterize all nontrivial scaling limits of solutions. Our results include, as a special case, the scaling limits for the classical Smoluchowski model with constant rate kernel , previously studied by Menon and Pego, among others. This is joint work with Gautam Iyer and Bob Pego. Submitted by
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