Stationary States and Asymptotic Behaviour of Aggregation Models with Nonlinear Local Repulsion
Analysis of PDEs
2014-03-17 v1
Abstract
We consider a continuum aggregation model with nonlinear local repulsion given by a degenerate power-law diffusion with general exponent. The steady states and their properties in one dimension are studied both analytically and numerically, suggesting that the quadratic diffusion is a critical case. The focus is on finite-size, monotone and compactly supported equilibria. We also investigate numerically the long time asymptotics of the model by simulations of the evolution equation. Issues such as metastability and local/ global stability are studied in connection to the gradient flow formulation of the model.
Keywords
Cite
@article{arxiv.1306.0930,
title = {Stationary States and Asymptotic Behaviour of Aggregation Models with Nonlinear Local Repulsion},
author = {Martin Burger and Razvan Fetecau and Yanghong Huang},
journal= {arXiv preprint arXiv:1306.0930},
year = {2014}
}