Gelation in coagulation and fragmentation models

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Convergence of the Marcus–Lushnikov Process (2004, background): “When K(x, y) ≥ c(xy + xy), with c > 0, α, β ∈ [0, 1], it is proved in Escobedo-Mishler-Perthame [7] that if α + β > 1, then gelation occurs in the Smoluchowski equation: there exists an instant Tgel < ∞ such that the mass consisting in infinite particles becomes positive.”
An introduction to mathematical models of coagulation–fragmentation processes: A discrete deterministic mean-field approach (2006, background): “[40] also prove the occurrence of gelation in systems with non-zero fragmentation terms.”
Existence of Self-Similar Solutions to Smoluchowski’s Coagulation Equation (2005, background): “More precisely, some mass can be lost in finite time, a phenomenon known as gelation, and the occurrence of gelation has been extensively studied recently, either by physicists (see [7, 18] and the references therein) and by mathematicians (see [9, 12] and the references therein).”
Well-posedness of Smoluchowski's coagulation equation for a class of homogeneous kernels (2006, background): “Nevertherless, under the additional assumption that a(x, y) ≥ κ2(xy) for some κ2 > 0, it follows from the analysis performed in [11, 7] that T∗ < ∞.”
Eigenelements of a General Aggregation-Fragmentation Model (2009, background): “(12) On the other hand, to avoid forming infinitely long polymers (gelation phenomenon, see [17, 18]), we assume lim x→+∞ xβ(x) τ(x) = +∞.”