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Large time behavior of nonlocal aggregation models with nonlinear diffusion
1.  Westfälische WilhelmsUniversität Münster, Institutfür Numerische und Angewandte Mathematik, Einsteinstr. 62, D 48149 Münster, Germany 
2.  Division of Mathematics for Engineering, Piazzale E. Pontieri, 2 Monteluco di Roio, 67040 L'Aquila, Italy 
Moreover, we also consider the behavior in the presence of nonlinear diffusion terms, the most interesting case being the one of small diffusion coefficients. Via the implicit function theorem we give a quite general proof of a rather natural assertion for such models, namely that there exist stationary solutions that have the form of a local peak around the center of mass. Our approach even yields the order of the size of the support in terms of the diffusion coefficients.
All these results are obtained via a reformulation of the equations considered using the Wasserstein metric for probability measures, and are carried out in the case of a single spatial dimension.
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