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We consider a continuum aggregation model with nonlinear local repulsiongiven by a degenerate power-law diffusion with general exponent. The steadystates and their properties in one dimension are studied both analytically andnumerically, suggesting that the quadratic diffusion is a critical case. Thefocus is on finite-size, monotone and compactly supported equilibria. We alsoinvestigate numerically the long time asymptotics of the model by simulationsof the evolution equation. Issues such as metastability and local/ globalstability are studied in connection to the gradient flow formulation of themodel.

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