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arXiv · 0904.2473

Existence, positivity and stability for a nonlinear model of cellular proliferation

Mostafa Adimy·Fabien Crauste
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Abstract

In this paper, we investigate a system of two nonlinear partial differential equations, arising from a model of cellular proliferation which describes the production of blood cells in the bone marrow. Due to cellular replication, the two partial differential equations exhibit a retardation of the maturation variable and a temporal delay depending on this maturity. We show that this model has a unique solution which is global under a classical Lipschitz condition. We also obtain the positivity of the solutions and the local and global stability of the trivial equilibrium.

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Mostafa Adimy, Fabien Crauste. 2009-04-16. Existence, positivity and stability for a nonlinear model of cellular proliferation. https://doi.org/10.1016/j.nonrwa.2004.09.001

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