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Seminar

Language	English
From	2012/01/20 15:30
To	2012/01/20 17:30
Place	Room 251, Building No.3, Faculty of Science, Kyoto University
Seminar Name	NLPDE Seminar
Title	Cauchy problem of the parabolic-parabolic Keller-Segel system on the plane
Field	Analysis
Speakers	Noriko Mizoguchi
Affiliation	Tokyo Gakugei University
Abstract	This talk is concerned with the existence of global solutions $(u,v)$ to Cauchy problem of the parabolic-parabolic Keller-Segel system on the plane, where $u$ and $v$ denote the density of cells and of chemical substance, respectively. There are a lot of papers of simplified chemotaxis system whose second equation is elliptic. In such a system, $8 \pi$ is a critical mass of $u$ that separates the blowup and the global existence. However the original system has not been quite studied. I show that if mass of $u$ is less than or equal to $8 \pi$ , then the solution exists globally in time. Moreover the existence of forward self-similar solutions with mass of $u$ greater than $8 \pi$ is mentioned.
Link	http://www.math.kyoto-u.ac.jp/~yosihiro/nlpde/nlpde.html