Theoretical derivations and analyses of the Fisher-Hotelling model on urban growth

Based on the hypotheses of Christaller Losch's central places and von Thunen's isolated city,the Fisher Hotelling model for urban diffusive growth,p/t=D 2p+Ap(s-p),is derived frotn the normal probability distibution on Brownian motion of population,p(x,y,t)=12πr 2 0texp-(x 2+y 2)/2r 2 0t,which links up with Sherratt's model on urban population densities,ρ(r)=ρ 0exp(-r 2/2r 2 0),and the Naroll Bertalanffy allometric relationship of temporal urban rural population distribution,u(t)∝ r(t) ...