Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type with small data
Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type with small data
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DOI：
10.1016/j.jde.2011.08.047
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发表时间：
2012-02
影响因子：
2.4
通讯作者：
Sachiko Ishida;T. Yokota
中科院分区：
文献类型：
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作者：
Sachiko Ishida;T. Yokota
本文研究“抛物线-抛物线”型拟线性简并凯勒-席格尔系统（KS）。当 q⩾m+2N（m 表示扩散强度，q 表示非线性）时，小初始数据的 (KS) 弱解的全局存在性成立。在“抛物线-椭圆”型系统中，Sugiyama 和 Kunii (2006) [13, 定理 3] 和 Sugiyama (2007) [12, 定理 2] 也给出了类似的结果；请注意，q=m+2N 对应于广义藤田临界指数。然而，对于“抛物线-抛物线”类型，q⩾m+2N 的超临界情况尚未解决。因此，本文对未解决的问题给出了答案。
This paper deals with the quasilinear degenerate Keller–Segel system (KS) of “parabolic–parabolic” type. The global existence of weak solutions to (KS) with small initial data is established when q⩾m+2N (m denotes the intensity of diffusion and q denotes the nonlinearity). In the system of “parabolic–elliptic” type, Sugiyama and Kunii (2006) [13, Theorem 3] and Sugiyama (2007) [12, Theorem 2] state the similar result; note that q=m+2N corresponds to generalized Fujitaʼs critical exponent. However, the super-critical case where q⩾m+2N has been unsolved for “parabolic–parabolic” type. Therefore this paper gives an answer to the unsolved problem.