WIAS Preprint No. 2637, (2019)

Bilinear coagulation equations


  • Heydecker, Daniel
  • Patterson, Robert I. A.

2010 Mathematics Subject Classification

  • 60K35 82C2 82C26


  • Coagulation, bilinear kernel, gelation, phase transition, Smoluchowski equation,, Flory equation, random graph




We consider coagulation equations of Smoluchowski or Flory type where the total merge rate has a bilinear form π(y) · Aπ (x) for a vector of conserved quantities π, generalising the multiplicative kernel. For these kernels, a gelation transition occurs at a finite time tg ∈ (0,∞), which can be given exactly in terms of an eigenvalue problem in finite dimensions. We prove a hydrodynamic limit for a stochastic coagulant, including a corresponding phase transition for the largest particle, and exploit a coupling to random graphs to extend analysis of the limiting process beyond the gelation time.

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