Pilant M, Rundell W
Math Popul Stud. 1991;3(1):3-20. doi: 10.1080/08898489109525320.
"This paper deals with an inverse problem in age-structured population dynamics; the recovery of an unknown initial age distribution. We attempt to recover this function from overposed data which consists of either the total population over a time interval equal to the maximum life span of the species or the age structure of the population at a fixed later time. Existence, uniqueness and continuous dependence of the initial distribution function on the data are addressed. Some numerical simulations are presented to illustrate the feasibility of recovery using the methods of the paper."
本文研究年龄结构种群动力学中的一个反问题;即恢复未知的初始年龄分布。我们试图从叠加数据中恢复这个函数,这些数据包括等于该物种最大寿命的一个时间区间内的总人口,或者在一个固定的较晚时间的种群年龄结构。文中讨论了初始分布函数对于数据的存在性、唯一性和连续依赖性。还给出了一些数值模拟以说明使用本文方法进行恢复的可行性。