On dams of finite capacity

Abstract

We shall consider the following mathematical model of dams of finite capacity. In the time interval (0, ∞) water is flowing into a dam (reservoir). Denote by χ(u) the total quantity of water flowing into the dam in the time interval (0, u). The capacity of the dam is a finite positive number h. If the dam becomes full, the excess water overflows. Denote by δ(u) the total quantity of water demanded in the time interval (0, u). If there is enough water in the reservoir the demand is satisfied, if there is not enough water the difference is supplied from elsewhere Denote by η(t) the content of the dam at time t. η(0) is the initial content.