Stationary states and asymptotic behavior of aggregation models with nonlinear local repulsion

Burger M, Fetecau R, Huang Y (2014)


Publication Language: English

Publication Type: Journal article

Publication year: 2014

Journal

Publisher: Society for Industrial and Applied Mathematics Publications

Book Volume: 13

Pages Range: 397-424

Issue: 1

DOI: 10.1137/130923786

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 numerically investigate 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. © 2014 Society for Industrial and Applied Mathematics.

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APA:

Burger, M., Fetecau, R., & Huang, Y. (2014). Stationary states and asymptotic behavior of aggregation models with nonlinear local repulsion. SIAM Journal on Applied Dynamical Systems, 13, 397-424. https://dx.doi.org/10.1137/130923786

MLA:

Burger, Martin, Razvan Fetecau, and Yanghong Huang. "Stationary states and asymptotic behavior of aggregation models with nonlinear local repulsion." SIAM Journal on Applied Dynamical Systems 13 (2014): 397-424.

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