Nonlinear, globally age-dependent population models: Some basic theory
type: Item
instance of: scholarly article
title: Nonlinear, globally age-dependent population models: Some basic theory
zbMATH Open document ID: 0579.92021
DOI: 10.1016/0022-247X(85)90044-7
author: Richard H. Elderkin
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: Basic theory is developed for the nonlinear age-dependent population equation \[ \partial u/\partial a+\partial u/\partial t=F(a,t,u(a,t),u(\cdot,t)),\quad u(0,t)=G(t,u(\cdot,t))=u_ 1(t),\quad u(a,0)=u_ 0(a). \] The method of characteristics is used to prove existence, uniqueness, and regularity of solutions under Lipschitz continuity assumptions on F and G and boundedness assumptions on \(u_ 0\) and \(u_ 1.\) Additional results concerning the monotonicity of the solution operator and the existence of steady states are established. A discussion is provided of various applications of models in epidemics, malaria innoculation, and seed dispersal.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35F25
Mathematics Subject Classification ID: 35F30
zbMATH DE Number: 3928785
zbMATH Keywords: nonlinear age-dependent population equation
zbMATH Keywords: method of characteristics
zbMATH Keywords: Lipschitz continuity assumptions
zbMATH Keywords: boundedness assumptions
zbMATH Keywords: monotonicity
zbMATH Keywords: existence of steady states
zbMATH Keywords: epidemics
zbMATH Keywords: malaria innoculation
zbMATH Keywords: seed dispersal
reviewed by: Glenn Webb
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3928785