Well-posedness of diffusion-aggregation equations with bounded kernels and their mean-field approximations
- Authors: Li Chen, Paul Nikolaev, David J. Prömel
- First public date: 2023-10-20
- arXiv: 2310.13463
- Preprint year: 2023
- Status: Published
- Publication type: Journal article
- Publication year: 2024
- Journal: Mathematical Methods in the Applied Sciences 47(11), 9222–9248 (2024)
- Publication details: Author’s publication list
- DOI: 10.1002/mma.10069
Abstract
The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence argument to treat the nonlinearity as well as a Moser iteration. Moreover, we prove a quantitative estimate in probability with arbitrary algebraic rate between the approximative interacting particle systems and the approximative McKean-Vlasov SDEs, which implies propagation of chaos for the interacting particle systems.