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Remarks on the global existence of weak solutions to quasilinear degenerate Keller-Segel systems

Pages: 345 - 354, Issue special, November 2013

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Sachiko Ishida - Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan (email)
Tomomi Yokota - Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan (email)

Abstract: The global existence of weak solutions to quasilinear ``degenerate'' Keller-Segel systems is shown in the recent papers [3], [4]. This paper gives some improvements and supplements of these. More precisely, the differentiability and the smallness of initial data are weakened when the spatial dimension $N$ satisfies $N\geq2$. Moreover, the global existence is established in the case $N=1$ which is unsolved in [4].

Keywords:  Quasilinear degenerate Keller-Segel systems, global existence.
Mathematics Subject Classification:  Primary: 35K57; Secondary: 35B33.

Received: August 2012;      Revised: December 2012;      Published: November 2013.

 References