期刊
SIAM JOURNAL ON APPLIED MATHEMATICS
卷 79, 期 4, 页码 1501-1527出版社
SIAM PUBLICATIONS
DOI: 10.1137/18M1163944
关键词
diffusion limit; biological diffusion; Fokker-Planck diffusion; Fickian diffusion
资金
- National Research Foundation of Korea [NRF-2017R1A2B2010398]
In this paper we derive diffusion equations in a heterogeneous environment. We consider a system of discrete kinetic equations that consists of two phenotypes of different turning frequencies. The two phenotypes change their states according to state transition frequencies which depend on the environment. We show that the density of the total population of the two phenotypes converges to the solution of a Fokker-Planck type diffusion equation if turning frequencies are of higher order than the state transition frequencies. If it is the other way around, i.e., if the state changes many times between each turning, the density converges to the solution of a Fickian diffusion equation.
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