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.