Existence results for a nonlinear version of Rotenberg model with infinite maturation velocities

In this paper, we present some existence results on L¹ spaces of a nonlinear boundary value problem derived from a model introduced by Rotenberg (1983) describing the growth of a cell population. Each cell of this population is distinguished by its degree of maturity μ ∈ 0,1] and its maturation velocity v. The biological boundary at μ = 0 and μ = 1 are fixed and tightly coupled through the mitosis. At mitosis, daughter cells and mother cells are related by a general reproduction rule, which covers all known biological ones. In this work, the maturation velocity is allowed to be infinite, that is, v ∈ 0, + ∞ ). This hypothesis introduce some mathematical difficulties, which are overcomed by using a measure of weak noncompactness adapted to the problem and a recent fixed point theorem (Theorem 3.2) involving weakly compact operators on nonreflexive Banach spaces. Copyright © 2014 John Wiley & Sons, Ltd.