# Global classical solvability and generic infinite-time blow-up in quasilinear Keller–Segel systems with bounded sensitivities

@article{Winkler2019GlobalCS, title={Global classical solvability and generic infinite-time blow-up in quasilinear Keller–Segel systems with bounded sensitivities}, author={M. Winkler}, journal={Journal of Differential Equations}, year={2019}, volume={266}, pages={8034-8066} }

Abstract The chemotaxis system (⋆) { u t = ∇ ⋅ ( D ( u , v ) ∇ u ) − ∇ ⋅ ( S ( u , v ) ∇ v ) , v t = Δ v − v + u , is considered under homogeneous Neumann boundary conditions in a bounded domain Ω ⊂ R n , n ≥ 2 , along with initial conditions involving suitably regular and nonnegative data. It is firstly asserted that if the positive smooth function D decays at most algebraically with respect to u, then for any smooth nonnegative and bounded S fulfilling a further mild assumption especially… Expand

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#### References

SHOWING 1-10 OF 40 REFERENCES

Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity

- Physics, Mathematics
- 2011

Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect

- Mathematics
- 2010

Global existence and slow grow-up in a quasilinear Keller–Segel system with exponentially decaying diffusivity

- Mathematics
- 2017

Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model

- Mathematics
- 2010