TITLE:
Non-Maxwellian Kinetic Modelling of City Size Distribution
AUTHORS:
Lijuan Yu, Jie Liao
KEYWORDS:
Variable Collision Kernel, Kinetic Fokker-Planck Equation, Generalized Gamma Distribution
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.6,
June
28,
2021
ABSTRACT: To extend the kinetic formulation of city size distribution introduced in [1], the non-Maxwellian kinetic modeling is introduced in the present study, in which a variable collision kernel is used in the underlying kinetic equation of Boltzmann type. By resorting to the well-known grazing asymptotic, a kinetic Fokker-Planck counterpart is obtained. The equilibrium of the Fokker-Planck equation belongs to the class of generalized Gamma distributions. Numerical test shows good fit of the generalized Gamma distribution with the city size distribution of China.