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

International audienceQualitative 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