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

Kenneth H.  Karlsen; Süleyman  Ulusoy

doi:10.3934/nhm.2016.11.181

Article Contents

2016, Volume 11, Issue 1: 181-201. Doi: 10.3934/nhm.2016.11.181

This issue Previous Article One-dimensional aggregation equation after blow up: Existence, uniqueness and numerical simulation Next Article

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

Kenneth H. Karlsen^1, and
Süleyman Ulusoy^2,

1.
Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo
2.
Department of Mathematics, Faculty of Education, Zirve University, Gaziantep, 27260

Received: March 31, 2015

Revised: June 30, 2015

Published: February 2016

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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.

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Mathematics Subject Classification: Primary: 35R09, 35L60, 35D; Secondary: 92C17.

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