Models of Discrete and Continuous Cell Differentiation in the Framework of Transport Equation

We introduce a class of structured population models describing cell differentiation that consists of discrete and continuous transitions. The model is defined in a framework of measure-valued solutions of a nonlinear transport equation with a growth term. To obtain ODE-type quasi-stationary node po...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 2012-01, Vol.44 (2), p.1103-1133
Main Authors: Gwiazda, Piotr, Jamróz, Grzegorz, Marciniak-Czochra, Anna
Format: Article
Language:English
Subjects:
Applied mathematics
Population
Radon
Stem cells
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Summary:We introduce a class of structured population models describing cell differentiation that consists of discrete and continuous transitions. The model is defined in a framework of measure-valued solutions of a nonlinear transport equation with a growth term. To obtain ODE-type quasi-stationary node points we exploit the idea of non-Lipschitz zeroes in the velocity. This, in combination with the so-called measure-transmission conditions, allows us to prove the existence and uniqueness of solutions. Since the analysis has biological motivations, we provide examples of its application.
ISSN:0036-1410
1095-7154
DOI:10.1137/11083294X