Existence results for a nonlinear version of Rotenberg model with infinite maturation velocities |
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| Authors: | Mounir Boumhamdi Khalid Latrach Ahmed Zeghal |
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| Affiliation: | 1. Faculté des Sciences et Techniques, Laboratoire de Mathématiques et Applications, Université Sultan Moulay Slimane, BP 523 Béni Mellal, Morocco;2. Laboratoire de Mathématiques, UMR 6620 ‐ CNRS, Université Blaise Pascal, Complexe des Cézeaux, BP 80026, 63171 Aubière, France |
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| Abstract: | 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. |
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| Keywords: | nonlinear transport equation boundary value problem measure of weak noncompactness fixed point theorem existence results |
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