A Fokker-Planck equation for growing cell populations
type: Item
instance of: scholarly article
title: A Fokker-Planck equation for growing cell populations
zbMATH Open document ID: 0644.92019
DOI: 10.1007/BF00275888
author: C. van der Mee
author: Paul F. Zweifel
published in: Journal of Mathematical Biology
publication date: 1987-01-01T00:00:00Z
review text: 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.
reviewed by: Gabriella Di Blasio
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 34A05
zbMATH DE Number: 4051415
zbMATH Keywords: model for cell growth
zbMATH Keywords: Airy functions
zbMATH Keywords: time dependent linear transport theory
zbMATH Keywords: closed form solutions
zbMATH Keywords: Fokker-Planck equation
zbMATH Keywords: degree of maturity
zbMATH Keywords: maturation velocity
zbMATH Keywords: reproduction equation
zbMATH Keywords: separation of variables
zbMATH Keywords: eigenfunction expansions
MaRDI profile type: Publication
Wikidata QID: Q52428630
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full work available at URL: https://doi.org/10.1007/bf00275888
OpenAlex ID: W1964566566
description: scientific article; zbMATH DE number 4051415