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On a hyperbolic Keller-Segel system with degenerate nonlinear fractional diffusion

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  • We investigate a Keller-Segel model with quorum sensing and a fractional diffusion operator. This model describes the collective cell movement due to chemical sensing with flux limitation for high cell densities and with anomalous media represented by a nonlinear, degenerate fractional diffusion operator. The purpose of this paper is to introduce and prove the existence of a properly defined entropy solution.
    Mathematics Subject Classification: Primary: 35R09, 35L60, 35D; Secondary: 92C17.

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