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Existence results for a nonlinear version of Rotenberg model with infinite maturation velocities
Author(s) -
Boumhamdi Mounir,
Latrach Khalid,
Zeghal Ahmed
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3187
Subject(s) - mathematics , fixed point theorem , nonlinear system , banach space , fixed point , population , measure (data warehouse) , boundary (topology) , boundary value problem , mathematical analysis , pure mathematics , calculus (dental) , demography , physics , computer science , quantum mechanics , medicine , dentistry , database , sociology
In this paper, we present some existence results on L 1 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.