# Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel

@inproceedings{Carrillo2021AsymptoticSO, title={Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel}, author={J. Carrillo and David G'omez-Castro and Yao Yao and C. Zeng}, year={2021} }

We give sharp conditions for the large time asymptotic simplification of aggregation-diffusion equations with linear diffusion. As soon as the interaction potential is bounded and its first and second derivatives decay fast enough at infinity, then the linear diffusion overcomes its effect, either attractive or repulsive, for large times independently of the initial data, and solutions behave like the fundamental solution of the heat equationwith some rate. The potentialW (x) ∼ log |x| for |x… Expand

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