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.
Authors with CRIS profile
Involved external institutions
Westfälische Wilhelms-Universität (WWU) Münster
Germany (DE)
Simon Fraser University
Canada (CA)
Imperial College London / The Imperial College of Science, Technology and Medicine
United Kingdom (GB)
Germany (DE)
Simon Fraser University
Canada (CA)
Imperial College London / The Imperial College of Science, Technology and Medicine
United Kingdom (GB)
How to cite
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://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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