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We study a mathematical model of cell populations dynamics proposed by M.Rotenberg and investigated by M. Boulanouar. Here, a cell is characterized byher maturity and speed of maturation. The growth of cell populations isdescribed by a partial differential equation with a boundary condition. In thefirst part of the paper we exploit semigroup theory approach and apply LordKelvin's method of images in order to give a new proof that the model is wellposed. Next, we use a semi-explicit formula for the semigroup related to themodel obtained by the method of images in order to give growth estimates forthe semigroup. The main part of the paper is devoted to the asymptoticbehaviour of the semigroup. We formulate conditions for the asymptoticstability of the semigroup in the case in which the average number of viabledaughters per mitosis equals one. To this end we use methods developed by K.Pich\'or and R. Rudnicki.

Lord Kelvin's method of images approach to the Rotenberg model and its asymptotics