caa a22 4500 44532984X CHVBK 20180317142733.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s00285-010-0357-5 doi (NATIONALLICENCE)springer-10.1007/s00285-010-0357-5 Large mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis [Elektronische Daten] [Piotr Biler, Lucilla Corrias, Jean Dolbeault] In two space dimensions, the parabolic-parabolic Keller-Segel system shares many properties with the parabolic-elliptic Keller-Segel system. In particular, solutions globally exist in both cases as long as their mass is less than a critical threshold M c. However, this threshold is not as clear in the parabolic-parabolic case as it is in the parabolic-elliptic case, in which solutions with mass above M c always blow up. Here we study forward self-similar solutions of the parabolic-parabolic Keller-Segel system and prove that, in some cases, such solutions globally exist even if their total mass is above M c, which is forbidden in the parabolic-elliptic case. Springer-Verlag, 2010 Keller-Segel model nationallicence Chemotaxis nationallicence Self-similar solution nationallicence Nonlocal parabolic equations nationallicence Critical mass nationallicence Existence nationallicence Blowup nationallicence Biler Piotr Instytut Matematyczny, Uniwersytet Wrocławski, pl.Grunwaldzki 2/4, 50-384, Wrocław, Poland aut Corrias Lucilla Département de Mathématiques, Université d'Évry Val d'Essonne, rue du père Jarlan, 91025, Évry Cédex, France aut Dolbeault Jean Ceremade (UMR CNRS 7534), Université Paris-Dauphine, Place de Lattre de Tassigny, 75775, Paris Cédex 16, France aut Journal of Mathematical Biology Springer-Verlag 63/1(2011-07-01), 1-32 0303-6812 63:1<1 2011 63 285 https://doi.org/10.1007/s00285-010-0357-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0357-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Biler Piotr Instytut Matematyczny, Uniwersytet Wrocławski, pl.Grunwaldzki 2/4, 50-384, Wrocław, Poland aut NATIONALLICENCE 700 1- Corrias Lucilla Département de Mathématiques, Université d'Évry Val d'Essonne, rue du père Jarlan, 91025, Évry Cédex, France aut NATIONALLICENCE 700 1- Dolbeault Jean Ceremade (UMR CNRS 7534), Université Paris-Dauphine, Place de Lattre de Tassigny, 75775, Paris Cédex 16, France aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 63/1(2011-07-01), 1-32 0303-6812 63:1<1 2011 63 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer