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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)

1 T. Hillen, K. J. Painter, A user's guide to PDE models for chemotaxis, J. Math. Biol. 58 (2009), 183-217.       
2 S. Ishida, A study on the solvability of degenerate Keller-Segel systems, Ph.D. thesis.
3 S. Ishida, T. Yokota, Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type, J. Differential Equations 252 (2012), 1421-1440.       
4 S. Ishida, T. Yokota, Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type with small data, J. Differential Equations 252 (2012), 2469-2491.       
5 E.F. Keller, L.A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theoret. Biol. 26 (1970), 399-415.
6 M. Nakao, Global solutions for some nonlinear parabolic equations with nonmonotonic perturbations, Nonlinear Anal. 10 (1986), 299-314.       
7 Y. Sugiyama, Global existence in the sub-critical cases and finite time blow-up in the super-critical cases to degenerate Keller-Segel systems, Differential Integral Equations 19 (2006), 841-876.       
8 Y. Sugiyama, H. Kunii, Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term, J. Differential Equations 227 (2006), 333-364.       
9 Y. Tao, M. Winkler, Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity, J. Differential Equations 252 (2012), 692-715.       
10 M. Winkler, Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model, J. Differential Equations 248 (2010), 2889-2905.       

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