scholarly journals On a two-phase size-structured population model with infinite states-at-birth and distributed delay in birth process

2014 ◽  
Vol 8 (1) ◽  
pp. 42-56 ◽  
Author(s):  
Meng Bai ◽  
Shihe Xu
Keyword(s):  
Population Model ◽  
Distributed Delay ◽  
Birth Process ◽  
Two Phase ◽  
Structured Population Model ◽  
Structured Population ◽  
Phase Size

Global existence of solutions for a nonlinear size-structured population model with distributed delay in the recruitment

2015 ◽  
Vol 26 (10) ◽  
pp. 1550085 ◽  
Author(s):  
Meng Bai ◽  
Shihe Xu
Keyword(s):  
Global Existence ◽  
Population Model ◽  
Initial Conditions ◽  
Local Existence ◽  
Extension Theorem ◽  
Distributed Delay ◽  
Structured Population Model ◽  
Structured Population ◽  
Global Existence Of Solutions ◽  
Local Existence And Uniqueness

In this paper, we study a nonlinear size-structured population model with distributed delay in the recruitment. The delayed problem is reduced into an abstract initial value problem of an ordinary differential equation in a Banach space by using the semigroup techniques. The local existence and uniqueness of solution as well as the continuous dependence on initial conditions are obtained by using the general theory of quasi-linear evolution equations in Banach spaces, while the global existence of solution is obtained by the estimates of the solution and the extension theorem.

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