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As a consequence, we recover the recent result about the global in time existence of weak solutions to the modified Patlak\u2013Keller\u2013Segel 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.<\/jats:p>","DOI":"10.1137\/070683337","type":"journal-article","created":{"date-parts":[[2008,2,4]],"date-time":"2008-02-04T11:37:29Z","timestamp":1202125049000},"page":"691-721","source":"Crossref","is-referenced-by-count":143,"title":["Convergence of the Mass-Transport Steepest Descent Scheme for the Subcritical Patlak\u2013Keller\u2013Segel Model"],"prefix":"10.1137","volume":"46","author":[{"given":"Adrien","family":"Blanchet","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vincent","family":"Calvez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jos\u00e9 A.","family":"Carrillo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,2,1]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.57262\/ade\/1355867881"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-004-0455-x"},{"key":"R3","unstructured":"L.A. Ambrosio, N. Gigli, and G. Savar\u00e9,\n                      Gradient Flows in Metric Spaces and in the Space of Probability Measures\n                      , Lectures in Math., Birkh\u00e4user, Cambridge, MA, 2005."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.2307\/2946638"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1997310506151"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023032000560"},{"key":"R7","unstructured":"A. Blanchet, J.A. Carrillo, and N. Masmoudi,\n                      Infinite time aggregation for the critical Patlak\u2013Keller\u2013Segel model in $\\RR^2$\n                      , Comm. Pure Appl. Math., to appear."},{"key":"R8","unstructured":"A. Blanchet, J. Dolbeault, and B. Perthame,\n                      Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions\n                      , Electron. J. 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