Boundedness in quasilinear Keller–Segel systems of parabolic–parabolic type on non-convex bounded domains

@article{Ishida2014BoundednessIQ,
  title={Boundedness in quasilinear Keller–Segel systems of parabolic–parabolic type on non-convex bounded domains},
  author={Sachiko Ishida and Kiyotaka Seki and T. Yokota},
  journal={Journal of Differential Equations},
  year={2014},
  volume={256},
  pages={2993-3010}
}
Abstract This paper deals with the quasilinear fully parabolic Keller–Segel system { u t = ∇ ⋅ ( D ( u ) ∇ u ) − ∇ ⋅ ( S ( u ) ∇ v ) , x ∈ Ω , t > 0 , v t = Δ v − v + u , x ∈ Ω , t > 0 , under homogeneous Neumann boundary conditions in a bounded domain Ω ⊂ R N with smooth boundary, N ∈ N . The diffusivity D ( u ) is assumed to satisfy some further technical conditions such as algebraic growth and D ( 0 ) ⩾ 0 , which says that the diffusion is allowed to be not only non-degenerate but also… Expand
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