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Article Dans Une Revue Mathematische Annalen Année : 2017

Blow-up behavior of solutions to a degenerate parabolic-parabolic Keller-Segel system

Résumé

Qualitative properties of solutions blowing up in finite time are obtained for a degenerate parabolic-parabolic Keller-Segel system, the nonlinear diffusion being of porous medium type with an exponent smaller or equal to the critical one $m_c := 2(N -1)/N$. In both cases, it is shown that only type~$II$ blow-up is possible, that is, blow-up at the same rate as backward self-similar solutions never occurs. Further information on the generation of singularities induced by mass concentration are given in the critical case.
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Dates et versions

hal-01589723 , version 1 (18-09-2017)

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Kazuhiro Ishige, Philippe Laurencot, Noriko Mizoguchi. Blow-up behavior of solutions to a degenerate parabolic-parabolic Keller-Segel system. Mathematische Annalen, 2017, 367, pp.461--499. ⟨10.1007/s00208-016-1400-7⟩. ⟨hal-01589723⟩
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