Asymptotic behavior for a cellular replication and maturation model

We consider a nonlocal first order partial differential equation with time delay that models simultaneous cell replication and maturation processes. We establish a comparison principle and construct monotone sequences to show the existence and uniqueness of the solution to the equation. We then anal...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2009-12, Vol.360 (2), p.727-736
Main Author: Deng, Keng
Format: Article
Language:English
Subjects:
Asymptotic behavior
Comparison principle
Delayed nonlocal transport equation
Exact sciences and technology
Existence–uniqueness
Mathematical analysis
Mathematics
Monotone sequences
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
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Summary:We consider a nonlocal first order partial differential equation with time delay that models simultaneous cell replication and maturation processes. We establish a comparison principle and construct monotone sequences to show the existence and uniqueness of the solution to the equation. We then analyze the asymptotic behavior of the solution via upper–lower solution technique.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.06.080