Journal article
TRAVELING WAVES IN A KELLER-SEGEL MODEL WITH LOGISTIC GROWTH
Communications in mathematical sciences, Vol.20(3), pp.829-853
01/01/2022
DOI: 10.4310/CMS.2022.v20.n3.a9
Abstract
Bacterial diffusion, proliferation and chemotactic aggregation play an important role in forming a traveling wave in a model for chemotaxis. In this paper, we investigate the existence and non-existence of traveling wave solutions of a Keller-Segel type model for chemotaxis, where logistic cell growth is considered and chemotactic sensitivity function is a general C-1 function that represents positive or negative chemotaxis. To show the existence of traveling waves, we use techniques from dynamical system theory. By applying the techniques, we determine the range of parameter values of the bacterial chemotaxis and the kinetics of cell and chemical for which traveling wave solutions exist. Furthermore, we examine the monotonicity of the traveling wave solutions. Finally, we conclude that the traveling waves are spectrally unstable.
Details
- Title: Subtitle
- TRAVELING WAVES IN A KELLER-SEGEL MODEL WITH LOGISTIC GROWTH
- Creators
- Tong Li - Univ Iowa, Dept Math, Iowa City, IA 52242 USAJeungeun Park - SUNY Coll New Paltz, Dept Math, New Paltz, NY 12561 USA
- Resource Type
- Journal article
- Publication Details
- Communications in mathematical sciences, Vol.20(3), pp.829-853
- Publisher
- Int Press Boston, Inc
- DOI
- 10.4310/CMS.2022.v20.n3.a9
- ISSN
- 1539-6746
- eISSN
- 1945-0796
- Number of pages
- 25
- Language
- English
- Date published
- 01/01/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984243929402771
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