Swarming in domains with boundaries: approximation and regularization by nonlinear diffusion
Analysis of PDEs
2018-09-05 v3 Adaptation and Self-Organizing Systems
Pattern Formation and Solitons
Abstract
We consider an aggregation model with nonlinear diffusion in domains with boundaries and investigate the zero diffusion limit of its solutions. We establish the convergence of weak solutions for fixed times, as well as the convergence of energy minimizers in this limit. Numerical simulations that support the analytical results are presented. A second key scope of the numerical studies is to demonstrate that adding small nonlinear diffusion rectifies a flaw of the plain aggregation model in domains with boundaries, which is to evolve into unstable equilibria (non-minimizers of the energy).
Cite
@article{arxiv.1711.03622,
title = {Swarming in domains with boundaries: approximation and regularization by nonlinear diffusion},
author = {Razvan C. Fetecau and Mitchell Kovacic and Ihsan Topaloglu},
journal= {arXiv preprint arXiv:1711.03622},
year = {2018}
}
Comments
Minor correction. This version will appear in Discrete Contin. Dyn. Syst. Ser. B