Networks and Heterogeneous Media (NHM)

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

Pages: 181 - 201, Volume 11, Issue 1, March 2016      doi:10.3934/nhm.2016.11.181

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Kenneth H. Karlsen - Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo, Norway (email)
Süleyman Ulusoy - Department of Mathematics, Faculty of Education, Zirve University, Gaziantep, 27260, Turkey (email)

Abstract: 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.

Keywords:  Keller-Segel system, hyperbolic equation, fractional diffusion, non-local diffusion, entropy solution, compactness, existence.
Mathematics Subject Classification:  Primary: 35R09, 35L60, 35D; Secondary: 92C17.

Received: April 2015;      Revised: July 2015;      Available Online: January 2016.