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}
}
  • M. Winkler
  • Published 2019
  • Mathematics
  • Journal of Differential Equations
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
Boundedness in a three-dimensional Keller-Segel-Stokes system with subcritical sensitivity
  • M. Winkler
  • Computer Science, Mathematics
  • Appl. Math. Lett.
  • 2021
Blow-up profiles in quasilinear fully parabolic Keller--Segel systems
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