Convergence of the mass-transport steepest descent scheme for the subcritical Patlak-Keller-Segel model
File(s)
Published version
Author(s)
Blanchet, Adrien
Calvez, Vincent
Carrillo, Jose A
Type
Journal Article
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 with this equation for subcritical 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 subcritical case. Moreover, we show how this method performs numerically in dimension one. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudoinverse of the cumulative distribution function. We demonstrate its capabilities to reproduce the blow-up of solutions for supercritical masses easily without the need of mesh-refinement.
Date Issued
2008-01-01
Citation
SIAM JOURNAL ON NUMERICAL ANALYSIS, 46, pp.{691-721}-{691-721}
ISSN
0036-1429
Publisher
SIAM PUBLICATIONS
Start Page
{691-721}
End Page
{691-721}
Journal / Book Title
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume
46
Issue
2
Copyright Statement
© 2008 Society for Industrial and Applied Mathematics. Unauthorized reproduction of this article is prohibited.
Description
04.02.15 KB. Ok to add published version to spiral, SIAM policy
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=000253815100006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Publication Status
Published
Article Number
2