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

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  • 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].
    Mathematics Subject Classification: Primary: 35K57; Secondary: 35B33.

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