Moving spike patterns in a chemotaxis model and oscillatory traveling waves in a traffic flow model
Year: 2025
Type: article
Abstract: For the first project, we prove rigorously the existence of moving spike patterns in an attractive chemotaxis model with small diffusion coefficient for the chemical. In the zero diffusion limit, ϵ → 0, we prove that the nonmonotone traveling wave solutions of the system with ϵ > 0 converge to those of the system with ϵ = 0. Moreover, we show that the traveling wave solutions are linearly unstable. We perform numerical simulations and find existence of the moving spike patterns when ϵ > 0. We confirm that as ϵ → 0 the traveling wave solutions of the system with ϵ > 0 converge to the traveling wave solutions of the system with ϵ = 0.
DOI: 10.25820/etd.007944
Author: Stone, Casey Anna
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6926954793
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