zbMATH — the first resource for mathematics

Notes on diffusion in collisionless medium. (English) Zbl 1047.82018
A collisionless continuous medium in Euclidean space is discussed, i.e. a continuum of free particles moving inertially, without interacting with each other. It is shown that the distribution density of such medium is weakly converging to zero as time increases indefinitely. In the case of Maxwell’s velocity distribution of particles, this density satisfies the well-known diffusion equation, the diffusion coefficient increasing linearly with time.

82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
37H10 Generation, random and stochastic difference and differential equations
70F45 The dynamics of infinite particle systems
Full Text: DOI