On the equations of age-dependent population dynamics

The aim of this work is to give a direct and constructive proof of existence and uniqueness of a global solution to the equations of age-dependent population dynamics introduced and considered by M. E. Gurtin & R. C. MacCamy in 3]. The linear theory was developed by F. R. Sharpe & A. J. Lotka 10] and A. G. McKendrick 8] (see also 1], 9]) and extended to the nonlinear case by M. E. Gurtin & R. C. MacCamy in 3] (see also 4] 5] 6]). In 3], the key of the proof of existence and uniqueness was to reduce the problem to a pair of integral equations. In fact, as we shall see, the problem can also be solved by a simple fixed point argument. To outline more clearly the ideas of the proof, we will first discuss the setting and the resolution of the linear case, and then we will generalize the results of 3].