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EXISTENCE RESULTS FOR A BOUNDARY VALUE PROBLEM ARISING IN GROWING CELL POPULATIONS

Département de Mathématiques, Université de Corse, 20250 Corte, France

and

Département de Mathématiques, Faculté des Sciences et Techniques de Béni-Méllal, Université Cadi Ayyad, B.P. 523, Béni-Méllal, Morocco

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https://doi.org/10.1142/S0218202503002350Cited by:12 (Source: Crossref)

Abstract

The aim of this article is to prove some results regarding the existence of solutions on L₁ spaces to 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 two parameters: its degree of maturity μ and its maturation velocity v. The biological boundary of μ = 0 and μ = a (a > 0) 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. Our proofs, based on topological methods, use essentially the specific properties of weakly compact sets on L₁ spaces.

Keywords:

AMSC: 92B05, 34K10, 45K05

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