Mathematics of traveling waves in chemotaxis --Review paper--
By Zhian Wang. 2012
153 citations recorded by the source corpus.
This article surveys the mathematical aspects of traveling waves of a class of chemotaxis models with logarithmic sensitivity, which describe a variety of biological or medical phenomena including bacterial chemotactic motion, initiation of angiogenesis and reinforced random walks. The survey is focused on the existence, wave speed, asymptotic decay rates, stability and chemical diffusion limits of traveling wave solutions. The main approaches are reviewed and related analytical results are given with sketchy proofs. We also develop some new results with detailed proofs to fill the gap existing in the literature. The numerical simulations of steadily propagating waves will be presented along the study. Open problems are proposed for interested readers to pursue.
Subfields: Modeling and Simulation, Molecular Biology, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/fe11383a88704de17ed63da5eebfdbd44fdd90ec
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Citations in the corpus
- Boundedness, blowup and critical mass phenomenon in competing chemotaxis (2016, background): “see [4,5,15,16,19,29,31,32,37,40,41] and the references therein, and review articles [13,18,39]).”
- Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion (2016, background): “the overview in [37] and references cited therein) and also their stability has been investigated ([19],[27]).”
- Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D (2017, background): “y type of cell kinetics, which is known to be vital for such effects in standard reaction-diffusion equations. For studies on existence and stability properties of traveling wave solutions of (1.1) see [32, 17, 20] and references therein. The results on global existence to systems of the form (1.1) ar”