期刊
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
卷 13, 期 1, 页码 397-424出版社
SIAM PUBLICATIONS
DOI: 10.1137/130923786
关键词
aggregation; integro-differential equation; energy; minimizer; steady states; asymptotic behavior
资金
- NSERC [PIN-341834]
- UK EPSRC [EP/K008404/1]
- EPSRC [EP/K008404/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K008404/1] Funding Source: researchfish
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.
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