A Fokker-Planck equation for growing cell populations
The purpose of the paper is to give closed form solutions to a Fokker- Planck equation for the number of cells with a certain degree of maturity as a function of maturation velocity v and time \(t: f_ t+vf_{\mu}=Df_{vv}\) (\(\mu\) is the degree of maturation and D a diffusion coefficient). The equation is supplemented with the boundary conditions \[ f_ v(\mu,v,t)|_{v=0}=0,\quad \lim_{v\to \infty}f(\mu,v,t)=0 \] and a reproduction equation (of several types). The method is based on the separation of variables and on eigenfunction expansions.
scientific article; zbMATH DE number 4051415