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
5 Citations

References

SHOWING 1-10 OF 45 REFERENCES
Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system
Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
An interpolation inequality and its application in Keller-Segel model
Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
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