PreprintCC BY 4.0arXiv
The Two-Component Becker-Döring System: Basic Properties
Abstract
The two-component Becker-Döring model is a two-dimensional coagulation-fragmentation equation that describes the dynamics of clusters built from two different types of monomers growing and shrinking through monomer interaction. We show the existence and mass conservation of solutions and give a partial result regarding uniqueness. Furthermore, we prove under the assumption of detailed balance the entropy equation, followed by a detailed study of the equilibrium states and relative entropies. We can determine the minimum of all relative entropies under sequences of fixed Type I and Type II masses and fully describe the minimising sequences in the weak* topology.
Related
- Long Time Behaviour of the Two-Component Becker-Döring System
- The Moreau-Yosida approximation of the Entanglement of Formation: basic properties and accuracy estimates
- Energy conservation of weak solutions and Onsager's conjecture for the two-component Camassa-Holm system
- A Riemann-Hilbert approach to the two-component modified Camassa-Holm system with step-like boundary conditions
- Hierarchical Laminates Cannot Reproduce All Effective Properties of Planar Two-Phase Composites: A Counterexample with a 16-Component Potential
BibTeX
@misc{scholten2026twocomponent,
title = {{The Two-Component Becker-Döring System: Basic Properties}},
author = {Jens Scholten},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29842},
eprint = {2609.29842},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29842},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Two-Component Becker-Döring System: Basic Properties
AU - Jens Scholten
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.29842
UR - https://arxiv.org/abs/2609.29842
AB - The two-component Becker-Döring model is a two-dimensional coagulation-fragmentation equation that describes the dynamics of clusters built from two different types of monomers growing and shrinking through monomer interaction. We show the existence and mass conservation of solutions and give a partial result regarding uniqueness. Furthermore, we prove under the assumption of detailed balance the entropy equation, followed by a detailed study of the equilibrium states and relative entropies. We can determine the minimum of all relative entropies under sequences of fixed Type I and Type II masses and fully describe the minimising sequences in the weak* topology.
ER -