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Article Dans Une Revue Axioms Année : 2021

Relaxation limit of the aggregation equation with pointy potential

Résumé

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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Dates et versions

hal-03235634 , version 1 (27-05-2021)

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Benoît Fabrèges, Frédéric Lagoutière, Tran Tien, Nicolas Vauchelet. Relaxation limit of the aggregation equation with pointy potential. Axioms, 2021, 10 (2), ⟨10.3390/axioms10020108⟩. ⟨hal-03235634⟩
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