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Blow-up in finite or infinite time for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type
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Gradient estimate for solutions to quasilinear non-degenerate Keller-Segel systems on $\mathbb{R}^N$
1. | Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan, Japan |
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show all references
References:
[1] |
Math. Z., 202 (1989), 219-250.
doi: 10.1007/BF01215256. |
[2] |
Monographs in Mathematics, 89. Birkhäuser Boston, Inc., Boston, MA, 1995. xxxvi+335 pp.
doi: 10.1007/978-3-0348-9221-6. |
[3] |
J. Math. Anal. Appl., 326 (2007), 1410-1426.
doi: 10.1016/j.jmaa.2006.03.080. |
[4] |
Comm. Partial Differential Equations, 22 (1997), 1647-1669.
doi: 10.1080/03605309708821314. |
[5] |
J. Differential Equations, 252 (2012), 1421-1440.
doi: 10.1016/j.jde.2011.02.012. |
[6] |
J. Theor. Biol., 26 (1970), 399-415. Google Scholar |
[7] |
Math. Ann., 312 (1998), 319-340.
doi: 10.1007/s002080050224. |
[8] |
(Russian) Translated from the Russian by S. Smith. Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence, R.I., 1968 xi+648 pp. |
[9] |
Princeton University Press, Princeton, New Jersey, 1970. |
[10] |
Differential Integral Equations, 19 (2006), 841-876. |
[11] |
Differential Integral Equations, 20 (2007), 133-180. |
[12] |
J. Differential Equations, 227 (2006), 333-364.
doi: 10.1016/j.jde.2006.03.003. |
[13] |
J. Differential Equations, 252 (2012), 692-715.
doi: 10.1016/j.jde.2011.08.019. |
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