Blow-up profiles and refined extensibility criteria in quasilinear Keller–Segel systems

@article{Freitag2018BlowupPA,
  title={Blow-up profiles and refined extensibility criteria in quasilinear Keller–Segel systems},
  author={M. Freitag},
  journal={Journal of Mathematical Analysis and Applications},
  year={2018},
  volume={463},
  pages={964-988}
}
  • M. Freitag
  • Published 2018
  • Mathematics
  • Journal of Mathematical Analysis and Applications
Abstract In this work we consider the system { u t = ∇ ⋅ ( D ( u ) ∇ u ) − ∇ ⋅ ( S ( u ) ∇ v ) in Ω × ( 0 , ∞ ) v t = Δ v − v + u in Ω × ( 0 , ∞ ) , for a bounded domain Ω ⊂ R n , n ≥ 2 , where the functions D and S behave similarly to power functions. We prove the existence of classical solutions under Neumann boundary conditions and for smooth initial data. Moreover, we characterise the maximum existence time T max of such a solution depending chiefly on the relation between the functions D… Expand

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