Global existence of weak solutions to quasilinear degenerate Keller–Segel systems of parabolic–parabolic type

This paper deals with the quasilinear degenerate Keller–Segel system (KS) of parabolic–parabolic type. The global existence of weak solutions to (KS) is established when (m denotes the intensity of diffusion and q denotes the nonlinearity) without restriction on the size of initial data; note that corresponds to generalized Fujitaʼs exponent. The result improves both Sugiyama (2007) [14, Theorem 1], and Sugiyama and Kunii (2006) [15, Theorem 1] in which it is assumed that q⩽m.