Abstract:
We study the Smoluchowski coagulation-fragmentation equation, which is an infinite set of non-linear ordinary differential equations describing the evolution of a mono-disperse system of particles in a well stirred solution. Approximating the solutions of the Smoluchowski equations by a sequence of finite Markov chains, we investigate the qualitative behavior of the solutions. We determine a device on the finite chains which can detect the gelation phenomena – the density dropping phenomena. It shows how the gelation phenomena are reflected on the sequence of finite Markov chains. Using this device, we determine various types of gelation kernels and get the bounds of gelation times.
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Received: 25 April 1997 / Accepted: 4 November 1997
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Jeon, I. Existence of Gelling Solutions for Coagulation-Fragmentation Equations. Comm Math Phys 194, 541–567 (1998). https://doi.org/10.1007/s002200050368
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DOI: https://doi.org/10.1007/s002200050368