A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up

@article{Bellomo2016ADC,
  title={A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up},
  author={Nicola Bellomo and Michael Winkler},
  journal={Communications in Partial Differential Equations},
  year={2016},
  volume={42},
  pages={436 - 473}
}
ABSTRACT This paper aims at providing a first step toward a qualitative theory for a new class of chemotaxis models derived from the celebrated Keller–Segel system, with the main novelty being that diffusion is nonlinear with flux delimiter features. More precisely, as a prototypical representative of this class we study radially symmetric solutions of the parabolic–elliptic system under the initial condition and no-flux boundary conditions in balls Ω⊂ℝn, where χ>0 and . The main results assert… Expand
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This paper is concerned with radially symmetric solutions of the parabolic-elliptic version of the Keller-Segel system with flux limitation, as given by ( ) ⎧⎨ ⎩ ut = ∇ · ( u∇u √ u2 + |∇u|2 ) − χ∇ ·Expand
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