Nonlinear, globally age-dependent population models: Some basic theory
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.
nonlinear age-dependent population equation
scientific article; zbMATH DE number 3928785