Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/200610
 Title: Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel Authors: Carrillo, Jose A.Gomez-Castro, DavidYao, Yao Zeng, Chongchun Keywords: math.APmath.AP35B40, 35B45, 35C06, 35Q92 Issue Date: 28-May-2021 Citation: Carrillo, Jose A., Gomez-Castro, David, Yao, Yao, Zeng, Chongchun (2021-05-28). Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel. ScholarBank@NUS Repository. Abstract: 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 equation with some rate. The potential $W(x) \sim \log |x|$ for $|x| \gg 1$ appears as the natural limiting case when the intermediate asymptotics change. In order to obtain such a result, we produce uniform-in-time estimates in a suitable rescaled change of variables for the entropy, the second moment, Sobolev norms and the $C^\alpha$ regularity with a novel approach for this family of equations using modulus of continuity techniques. URI: https://scholarbank.nus.edu.sg/handle/10635/200610 Appears in Collections: Staff PublicationsElements

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