本篇論文，主要是介紹在年齡有限的情況下，建立具有年齡結構的連續人口線性模型，並找出其相對應的半群及無限小生成子。

The purpose of this paper is to set up a linear age-dependent population model with finite 
age range. We shall view the model as an abstract evolution equation in the Banach space L1
and associate with its solutions a strongly continuous semigroup of linear operator in this  
space.

Contents
1 Introduction…………………………………………………1
2 The Model and Solutions………………………………….2
3 The Semigroup associated with Solution………………4
Reference                                          12

[1] T.R. Malthus, An Essay on the principle of population (frist edition), printed for J. Johnson in St. Paul’s Churchyard, London,1798.
[2] A. G. Mckendrick, Applications of mathematics to medical problems, Proc. Edin. Math. Soc. 44 (1926), 98-130.
[3] J. Prüss, Equilibrium solutions of age-specific population dynamics of several species, J. math. biol. 11 (1981), 65-84.
[4] J. Prüss, On the qualitative behavior of population with age-specific interactions, Internatl J, Comput. Math. Appl. 9,No. 3 (1983), 327-339.
[5] J. Prüss, Stability analysis for equilibria in age-specific population dynamics, Nonlinear Anal. TMA 7 (1983), 1291-1313.
[6] A. E. Taylor, Introduction to functional Analysis, JohnWiley, New York, 1967
[7] P. F. Verhulst, Notice sur la loi que la population suit dans son accroissement, Correspondances Mathematique et physique 10 (1838), 113-121.
[8] G. F. Webb, Compactness of bounded trajectories of dynamical systems in infinite dimensional spaces, Proc. Roy. Edin. 84A (1979), 19-33.
[9] G. F. Webb, Nonlinear  semigroup and age-dependent population models, Ann. Mat. Pura appl. CXXIXX (1981), 43-55.
[10] G. F. Webb, Nonlinear age-dependent population dynamics in L1 , J. Integral Equations 5, No 4 (1983), 309-328.
[11] G. F. Webb, The semigroup associated with nonlinear age-dependent population dynamics, Int. J. Computers Appl. Math. 9 (1983), 487-497.