Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system

@article{Lankeit2017InfiniteTB,
  title={Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system},
  author={Johannes Lankeit},
  journal={arXiv: Analysis of PDEs},
  year={2017}
}
We consider a parabolic-elliptic chemotaxis system generalizing \[ \begin{cases}\begin{split} & u_t=\nabla\cdot((u+1)^{m-1}\nabla u)-\nabla \cdot(u(u+1)^{\sigma-1}\nabla v)\\ & 0 = \Delta v - v + u \end{split}\end{cases} \] in bounded smooth domains $\Omega\subset \mathbb{R}^N$, $N\ge 3$, and with homogeneous Neumann boundary conditions. We show that *) solutions are global and bounded if ${\sigma}<m-\frac{N-2}N$ *) solutions are global if $\sigma \le 0$ *) close to given radially… Expand
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