EXISTENCE RESULTS FOR A BOUNDARY VALUE PROBLEM ARISING IN GROWING CELL POPULATIONS-Reference-Cited by-同舟云学术

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

Published:2003-01 Issue:01 Volume:13 Page:1-17
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

LATRACH KHALID¹,ZEGHAL AHMED²

Affiliation:

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

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

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202503002350

Reference16 articles.

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2. A. Dehici, A. Jeribi and K. Latrach, On a transport operator arising in growing cell populations I. Spectral analysis, Advances in Math. Research, ed. G. Oyibo (Nova Sci. Publishers, 2002) pp. 159–186.

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