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

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

2009-04-16

arxiv.org/abs/0904.2473v1

Nonlinear Analysis Real World Applications 6, 2 (2005) 337-366

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.nonrwa.2004.09.001

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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