# Blow-up profiles in quasilinear fully parabolic Keller--Segel systems

@article{Fuest2019BlowupPI,
title={Blow-up profiles in quasilinear fully parabolic Keller--Segel systems},
author={Mario Fuest},
journal={arXiv: Analysis of PDEs},
year={2019}
}
• Mario Fuest
• Published 2019
• Mathematics, Physics
• arXiv: Analysis of PDEs
We examine finite-time blow-up solutions $(u, v)$ to \begin{align} \label{prob:star} \tag{$\star$} \begin{cases} u_t = \nabla \cdot (D(u, v) \nabla u - S(u, v) \nabla v), v_t = \Delta v - v + u \end{cases} \end{align} in a ball $\Omega \subset \mathbb R^n$, $n \ge 2$, where $D$ and $S$ generalize the functions \begin{align*} D(u, v) = (u+1)^{m-1} \quad \text{and} \quad S(u, v) = u (u+1)^{q-1} \end{align*} with $m, q \in \mathbb R$. We show that if $m \gt \frac{n-2}{n}$ as well as \$m-q \gt… Expand
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