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arXiv · 1306.0930

Stationary States and Asymptotic Behaviour of Aggregation Models with Nonlinear Local Repulsion

Martin Burger·Razvan Fetecau·Yanghong Huang
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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.

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Martin Burger, Razvan Fetecau, Yanghong Huang. 2013-06-04. Stationary States and Asymptotic Behaviour of Aggregation Models with Nonlinear Local Repulsion. https://arxiv.org/abs/1306.0930

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