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Large mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis.
MedLine Citation:
PMID:  20730434     Owner:  NLM     Status:  In-Data-Review    
Abstract/OtherAbstract:
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.
Authors:
Piotr Biler; Lucilla Corrias; Jean Dolbeault
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Publication Detail:
Type:  Journal Article     Date:  2010-08-22
Journal Detail:
Title:  Journal of mathematical biology     Volume:  63     ISSN:  1432-1416     ISO Abbreviation:  J Math Biol     Publication Date:  2011 Jul 
Date Detail:
Created Date:  2011-06-14     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7502105     Medline TA:  J Math Biol     Country:  Germany    
Other Details:
Languages:  eng     Pagination:  1-32     Citation Subset:  IM    
Affiliation:
Instytut Matematyczny, Uniwersytet Wrocławski, pl.Grunwaldzki 2/4, 50-384, Wrocław, Poland, Piotr.Biler@math.uni.wroc.pl.
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