Traveling wave solutions for a bacteria system with density-suppressed motility | Zendy

Roger Lui | Zendy; Hirokazu Ninomiya | Zendy

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Traveling wave solutions for a bacteria system with density-suppressed motility

Author(s) -

Roger Lui,

Hirokazu Ninomiya

Publication year - 2018

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2018213

Subject(s) - traveling wave , diffusion , bacteria , heuristic , constant (computer programming) , reaction–diffusion system , population , simple (philosophy) , biological system , component (thermodynamics) , mathematical proof , physics , biology , computer science , mathematics , mathematical analysis , mathematical optimization , thermodynamics , medicine , genetics , philosophy , geometry , environmental health , epistemology , programming language

In 2011, Liu et. al. proposed a three-component reaction-diffusion system to model the spread of bacteria and its signaling molecules (AHL) in an expanding cell population. At high AHL levels the bacteria are immotile, but diffuse with a positive diffusion constant at low distributions of AHL. In 2012, Fu et. al. studied a reduced system without considering nutrition and made heuristic arguments about the existence of traveling wave solutions. In this paper we provide rigorous proofs of the existence of traveling wave solutions for the reduced system under some simple conditions of the model parameters.

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