Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model
Blanchet, Adrien (Centre de Recerca Matemàtica)
Calvez, Vincent (ENS. Departement de Mathématiques et Applications (París, França))
Carrillo de la Plata, José Antonio (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Imprint: Centre de Recerca Matemàtica 2007
Description: 37 p.
Abstract: Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.
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 Creative Commons
Language: Anglès
Series: Centre de Recerca Matemàtica. Prepublicacions
Series: Prepublicacions del Centre de Recerca Matemàtica ; 738
Document: article ; submittedVersion
Subject: Equacions diferencials parcials

Adreça alternativa: https://hdl.handle.net/2072/4229


37 p, 656.7 KB

The record appears in these collections:
Research literature > Preprints

 Record created 2009-07-13, last modified 2020-11-21



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