Home > Research literature > Preprints > Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities |
Imprint: | Centre de Recerca Matemàtica 2010 |
Description: | 18 p. |
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 onedimensional equation is a contraction with respect to Fourier distance in the subcritical case. |
Rights: | Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús |
Language: | Anglès |
Series: | Centre de Recerca Matemàtica. Prepublicacions |
Series: | Prepublicacions del Centre de Recerca Matemàtica ; 958 |
Document: | article ; submittedVersion |
Subject: | Desigualtats (Matemàtica) ; Equacions diferencials |
18 p, 272.6 KB |