| Abstract: |
| We study long-time behavior of cluster-size distributions for the Smoluchowski coagulation equation with time-dependent injection of mass, in the critical case when the rate kernel is additive in cluster sizes. Scaled by an expected cluster size, solutions converge to the same self-similar profile for a great variety of injection schedules, corresponding to mass growth histories that are constant, power law, exponential, and double exponential, e.g. Key ingredients in the analysis are: an improved continuity theorem for Bernstein transforms (aka Laplace exponents), and scaling analysis of characteristics for the PDE that transforms satsify. |
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