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An existence and uniqueness principle for a nonlinear version of the Lebowitz‐Rubinow model with infinite maximum cycle length
Author(s) -
ArizaRuiz David,
GarciaFalset Jesús,
Latrach Khalid
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4622
Subject(s) - uniqueness , mathematics , nonlinear system , population , boundary value problem , population model , maximum principle , boundary (topology) , mathematical analysis , calculus (dental) , mathematical optimization , optimal control , medicine , physics , demography , dentistry , quantum mechanics , sociology
The present article deals with existence and uniqueness results for a nonlinear evolution initial‐boundary value problem, which originates in an age‐structured cell population model introduced by Lebowitz and Rubinow (1974) describing the growth of a cell population. Cells of this population are distinguished by age a and cycle length l . In our framework, daughter and mother cells are related by a general reproduction rule that covers all known biological ones. In this paper, the cycle length l is allowed to be infinite. This hypothesis introduces some mathematical difficulties. We consider both local and nonlocal boundary conditions.