arXiv subjects
Publications and source records attributed to William Kyle Barker.
The goal of this paper is to investigate the traveling wave solutions with one-sided far field conditions for the one-dimensional hyperbolic Keller-Segel equations with quorum sensitivity. The traveling wave solutions are piece-wise smooth in the moving coordinate, and satisfy the entropy inequality at the discontinuity.
This paper is concerned with traveling waves to an diffusive SIR model with delay placed in the diffusion terms as well as nonlinear incidence rate with delay. Using a cross iteration scheme and partial monotone conditions it will be shown that the existence of quasi upper and lower solutions is a sufficient condition for the existence of a traveling wave front. This will be shown via Schauder's fixed point theorem. Given an appropriate basic reproduction number the traveling wave front will flow from a disease-free steady state to endemic steady state. The construction of quasi upper and lower solutions will be carried out for a specific model.