Rigorous Derivation of the Degenerate Parabolic-Elliptic Keller-Segel System from a Moderately Interacting Stochastic Particle System. Part II Propagation of Chaos

• DOI: 10.48550/arxiv.2302.08763
• Publication Date: 2023-01-01
• Authors: Li Chen; Veniamin Gvozdik; Alexandra Holzinger; Yue Li
• Keywords: Particle system; Degeneracy (biology); Regularization

This work is a series of two articles. The main goal to rigorously derive the degenerate parabolic-elliptic Keller-Segel system in sub-critical regime from moderately interacting stochastic particle system. In first article [7], we establish classical solution theory and its non-local version. second article, which current one, propagation chaos result, where obtained used required estimates for Due degeneracy non-linear diffusion singular aggregation effect system, perform an approximation by using cut-offed potential. An additional linear on level as parabolic regularization We present result with logarithmic scalings. Consequently, follows directly convergence sense expectation vanishing viscosity argument