Refined Asymptotics for the subcritical Keller-Segel system and Related Functional InequalitiesReportar como inadecuado




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1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées 2 NUMED - Numerical Medicine UMPA-ENSL - Unité de Mathématiques Pures et Appliquées, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan Villeurbanne 3 Departament de Matemàtiques Barcelona

Abstract : We analyze the rate of convergence towards self-similarity for the subcritical Keller-Segel system in the radially symmetric two-dimensional case and in the corresponding one-dimensional case for logarithmic interaction. We measure convergence in Wasserstein distance. The rate of convergence towards self-similarity does not degenerate as we approach the critical case. As a byproduct, we obtain a proof of the logarithmic Hardy-Littlewood-Sobolev inequality in the one dimensional and radially symmetric two dimensional case based on optimal transport arguments. In addition we prove that the one-dimensional equation is a contraction with respect to Fourier distance in the subcritical case.

Keywords : Keller-Segel Long-time Asymptotics Self-similarity Wasserstein Distance Contraction





Autor: Vincent Calvez - José Antonio Carrillo -

Fuente: https://hal.archives-ouvertes.fr/



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