We establish a quantitative propagation of chaos for a large stochastic systems of interacting particles. We rigorously derive a mean-field system, which is a diffusive cell-to-cell nonlocal adhesion model for two different phenotypes of tumors, from that stochastic system as the number of particles tends to infinity. We estimate the error between the solutions to a N-particle Liouville equation associated with the particle system and the limiting mean-field system by employing the relative entropy argument.
|Journal||Journal of Nonlinear Science|
|Publication status||Published - 2022 Dec|
Bibliographical noteFunding Information:
We would like to sincerely thank the anonymous referee for helpful comments and suggestions. We thank Guang Yang for helpful conversations about showing the non-positivity of () based on probabilistic arguments. J. Ahn was supported by the Dongguk University Research Fund of 2020. M. Chae was supported by NRF-2018R1A1A3A04079376. Y.-P. Choi was supported by National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2017R1C1B2012918 and 2022R1A2C1002820) and Yonsei University Research Fund of 2021-22-0301. J. Lee is supported by SSTF-BA1701-05 (Samsung Science and Technology Foundation).
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Applied Mathematics