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

✍ Scribed by Mostafa Adimy; Fabien Crauste

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
296 KB
Volume
6
Category
Article
ISSN
1468-1218

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✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

Existence and positivity of solutions of
Existence and positivity of solutions of a fourth-order nonlinear PDE describing interface fluctuations
✍ Pavel M. Bleher; Joel L. Lebowitz; Eugene R. Speer πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 799 KB

## Abstract We study the partial differential equation magnified image which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case Γ— R __S__^1^. We establish existence, uniq