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• W2985453069 abstract "Abstract Inspired by recent work on minimizers and gradient flows of constrained interaction energies, we prove that these energies arise as the slow diffusion limit of well-known aggregation-diffusion energies. We show that minimizers of aggregation-diffusion energies converge to a minimizer of the constrained interaction energy and gradient flows converge to a gradient flow. Our results apply to a range of interaction potentials, including singular attractive and repulsive-attractive power-law potentials. In the process of obtaining the slow diffusion limit, we also extend the well-posedness theory for aggregation-diffusion equations and Wasserstein gradient flows to admit a wide range of nonconvex interaction potentials. We conclude by applying our results to develop a numerical method for constrained interaction energies, which we use to investigate open questions on set valued minimizers." @default.
• W2985453069 created "2019-11-22" @default.
• W2985453069 creator A5023507368 @default.
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• W2985453069 date "2020-04-01" @default.
• W2985453069 modified "2023-09-27" @default.
• W2985453069 title "Aggregation-diffusion to constrained interaction: Minimizers & gradient flows in the slow diffusion limit" @default.
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• W2985453069 doi "https://doi.org/10.1016/j.anihpc.2019.10.003" @default.
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