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

Kenneth H. Karlsen | Zendy; Süleyman Ulusoy | Zendy

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

Author(s) -

Kenneth H. Karlsen,

Süleyman Ulusoy

Publication year - 2016

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2016.11.181

Subject(s) - degenerate energy levels , nonlinear system , operator (biology) , diffusion , entropy (arrow of time) , anomalous diffusion , mathematics , mathematical analysis , computer science , physics , innovation diffusion , thermodynamics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene , knowledge management

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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