Dynamics of a kinetic model describing protein exchanges in a cell population
Abstract
We consider a cell population structured by a positive real number, describing the number of Pglycoproteins carried by the cell. We are interested in the effect of those proteins on the growth of the population: those proteins are indeed involve in the resistance of cancer cells to chemotherapy drugs. To describe this dynamics, we introduce a kinetic model. We then introduce a rigorous hydrodynamic limit, showing that if the exchanges are frequent, then the dynamics of the model can be described by a system of two coupled differential equations. Finally, we also show that the kinetic model converges to a unique limit in large times. The main idea of this analysis is to use Wasserstein distance estimates to describe the effect of the kinetic operator, combined to more classical estimates on the macroscopic quantities.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 arXiv:
 arXiv:1511.02665
 Bibcode:
 2015arXiv151102665M
 Keywords:

 Mathematics  Analysis of PDEs;
 35B40;
 35B35;
 35Q92;
 92D25;
 92D40