Li, Tong; Park, Jeungeun Traveling waves in a chemotaxis model with logistic growth. (English) Zbl 1423.35060 Discrete Contin. Dyn. Syst., Ser. B 24, No. 12, 6465-6480 (2019). Summary: Traveling wave solutions of a chemotaxis model with a reaction term are studied. We investigate the existence and non-existence of traveling wave solutions in certain ranges of parameters. Particularly for a positive rate of chemical growth, we prove the existence of a heteroclinic orbit by constructing a positively invariant set in the three dimensional space. The monotonicity of traveling waves is also analyzed in terms of chemotaxis, reaction and diffusion parameters. Finally, the traveling wave solutions are shown to be linearly unstable. Cited in 8 Documents MSC: 35C07 Traveling wave solutions 35B35 Stability in context of PDEs 35K57 Reaction-diffusion equations 92C17 Cell movement (chemotaxis, etc.) 35K45 Initial value problems for second-order parabolic systems 35K59 Quasilinear parabolic equations 35Q92 PDEs in connection with biology, chemistry and other natural sciences Keywords:reaction-diffusion-chemotaxis; cell growth; linear instability; reaction term; heteroclinic orbit PDFBibTeX XMLCite \textit{T. Li} and \textit{J. Park}, Discrete Contin. Dyn. Syst., Ser. B 24, No. 12, 6465--6480 (2019; Zbl 1423.35060) Full Text: DOI