Blow-up dynamics of self-attracting diffusive particles driven by competing convexities
Dynamical Systems
2013-01-31 v1 Numerical Analysis
Abstract
In this paper, we analyze the dynamics of an particles system evolving according the gradient flow of an energy functional. The particle system is a consistent approximation of the Lagrangian formulation of a one parameter family of non-local drift-diffusion equations in one spatial dimension. We shall prove the global in time existence of the trajectories of the particles (under a sufficient condition on the initial distribution) and give two blow-up criteria. All these results are consequences of the competition between the discrete entropy and the discrete interaction energy. They are also consistent with the continuous setting, that in turn is a one dimension reformulation of the parabolic-elliptic Keller-Segel in high dimensions.
Cite
@article{arxiv.1301.7075,
title = {Blow-up dynamics of self-attracting diffusive particles driven by competing convexities},
author = {V. Calvez and L. Corrias},
journal= {arXiv preprint arXiv:1301.7075},
year = {2013}
}