2022/08/07 by Mingying Zhong, Zhong, Mingying · 1 citation
Economics, Econometrics and Finance · Mathematics · #76P05 #82C40 #82D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Mathematical Biology Tumor Growth #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2208.03627
openalex publication_date 2022/08/07 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The pointwise space-time behaviors of the Green's function and the global solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system in spatial three dimension are studied in this paper. It is shown that the Green's function consists of the diffusion waves decaying exponentially in time but algebraically in space, and the singular kinetic waves which become smooth for all (t,x,v) when t>0. Furthermore, we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green's function.