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On the solvability of a nonlinear boundary value problem arising in the theory of growing cell populations

✍ Scribed by K. Latrach; M. A. Taoudi; A. Zeghal

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 153 KB
Volume: 28
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.615

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✦ Synopsis

Abstract

In this paper we establish some results regarding the existence of solution on L~1~ spaces to a nonlinear boundary value problem originally proposed by Lebowitz and Rubinow (J. Math. Biol. 1974; 1:17–36) to model an age‐structured proliferating cell population. Our approach, based on topological methods, uses essentially the specific properties of weakly compact sets on L~1~ spaces. Our results provide positive answers to the questions posed in Jeribi (Nonlinear Anal. Real World Appl. 2002; 3:85–105). Copyright © 2005 John Wiley & Sons, Ltd.

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