Well-posedness of a nonlinear model of proliferating cell populations with inherited cycle length

This paper deals with a nonlinear initial boundary values problem derived from a modified version of the so called Lebowitz and Rubinow's model [16] discussed in [8, 9] modeling a proliferating age structured cell population with inherited properties. We give existence and uniqueness results on appropriate weighted Lp-spaces with 1 ≤ p < ∞ in the case where the rate of cells mortality σ and the transition rate k are depending on the total density of population. General local and nonlocal reproduction rules are considered.