Splitting Schemes & Segregation In Reaction-(Cross-)Diffusion Systems
Analysis of PDEs
2017-11-16 v1
Abstract
One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint supports. We analyse such a reaction cross-diffusion system. In order to prove existence of weak solutions for a wide class of initial data without restriction about their supports or their positivity, we propose a variational splitting scheme combining ODEs with methods from optimal transport. In addition, this approach allows us to prove conservation of segregation for initially segregated data even in the presence of vacuum.
Cite
@article{arxiv.1711.05434,
title = {Splitting Schemes & Segregation In Reaction-(Cross-)Diffusion Systems},
author = {José A. Carrillo and Simone Fagioli and Filippo Santambrogio and Markus Schmidtchen},
journal= {arXiv preprint arXiv:1711.05434},
year = {2017}
}