Absence of gelation and regularity for coagulation-fragmentation-diffusion equations with critical coagulation rate in low dimension
Year: 2026
Type: preprint
Abstract: We consider a discrete coagulation-fragmentation-diffusion system on a bounded domain of $\mathbb{R}^d$. In dimension $d\leq 2$, we prove mass conservation (that is absence of gelation) when the coagulation coefficient satisfies the critical additive bound $a_{i, j} \leq C(i + j)$ for some constant $C > 0$. We thereby close the remaining gap between the spatially homogeneous setting and the spatially inhomogeneous diffusive setting. In dimension $d\leq 4$, we impose a higher decay rate on the coagulation and fragmentation coefficients, but we nonetheless prove regularity and absence of gelation under mild assumptions on the diffusion rates.
Source: arXiv (Cornell University)
Author: Bouton, Hector
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213805079