PreprintCC BY 4.0HAL
Absence of gelation and regularity for coagulation-fragmentation-diffusion equations with critical coagulation rate in low dimension
Abstract
We consider a discrete coagulation-fragmentation-diffusion system on a bounded domain of ℝd. In dimension d≤ 2, we prove mass conservation (that is absence of gelation) when the coagulation coefficient satisfies the critical additive bound ai, j ≤ 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≤ 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.
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BibTeX
@misc{bouton2026absence,
title = {{Absence of gelation and regularity for coagulation-fragmentation-diffusion equations with critical coagulation rate in low dimension}},
author = {Hector Bouton},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22399},
eprint = {2609.22399},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05753628v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Absence of gelation and regularity for coagulation-fragmentation-diffusion equations with critical coagulation rate in low dimension
AU - Hector Bouton
PY - 2026
DA - 2026/09/17
PB - HAL
DO - 10.48550/arxiv.2609.22399
UR - https://hal.science/hal-05753628v1
AB - We consider a discrete coagulation-fragmentation-diffusion system on a bounded domain of ℝ^d. In dimension d≤ 2, we prove mass conservation (that is absence of gelation) when the coagulation coefficient satisfies the critical additive bound a_i, j ≤ 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≤ 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.
ER -