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Relaxation limit of the aggregation equation with pointy potential

Abstract : This work is devoted to the study of a relaxation limit of the so-called aggregation equation with a pointy potential in one dimensional space. The aggregation equation is by now widely used to model the dynamics of a density of individuals attracting each other through a potential. When this potential is pointy, solutions are known to blow up in final time. For this reason, measure-valued solutions have been defined. In this paper, we investigate an approximation of such measure-valued solutions thanks to a relaxation limit in the spirit of Jin and Xin. We study the convergence of this approximation and give a rigorous estimate of the speed of convergence in one dimension with the Newtonian potential. We also investigate the numerical discretization of this relaxation limit by uniformly accurate schemes.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03235634
Contributor : Nicolas Vauchelet <>
Submitted on : Thursday, May 27, 2021 - 10:40:02 AM
Last modification on : Monday, June 28, 2021 - 2:26:06 PM

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  • HAL Id : hal-03235634, version 1
  • ARXIV : 2105.13820

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Benoît Fabrèges, Frédéric Lagoutière, Tran Tien, Nicolas Vauchelet. Relaxation limit of the aggregation equation with pointy potential. 2021. ⟨hal-03235634⟩

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