Boundedness of large-time solutions to a chemotaxis model with nonlocal and semilinear flux

@article{Burczak2014BoundednessOL,
  title={Boundedness of large-time solutions to a chemotaxis model with nonlocal and semilinear flux},
  author={Jan Burczak and Rafael Granero-Belinch'on},
  journal={Topological Methods in Nonlinear Analysis},
  year={2014},
  volume={47},
  pages={369-387}
}
A semilinear version of parabolic-elliptic Keller--Segel system with the \emph{critical} nonlocal diffusion is considered in one space dimension. We show boundedness of weak solutions under very general conditions on our semilinearity. It can degenerate, but has to provide a stronger dissipation for large values of a solution than in the critical linear case or we need to assume certain (explicit) data smallness. Moreover, when one considers a~logistic term with a parameter $r$, we obtain our… 
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