Travelling wave solutions of the density-suppressed motility model
Jing Li, Zhi-An Wang
TL;DR
This paper investigates traveling wave solutions in a density-suppressed motility model, revealing how self-trapping mechanisms lead to pattern formations consistent with experimental observations.
Contribution
It establishes the existence of minimal wave speed traveling wavefronts and provides numerical simulations matching experimental patterns.
Findings
Existence of traveling wavefronts with minimal wave speed
Numerical simulations align with experimental patterns
Self-trapping induces observable spatio-temporal patterns
Abstract
In this paper, we study the traveling wave solutions to the density-suppressed motility model describing the ``self-trapping'' mechanism that induces spatio-temporal pattern formations observed in the experiment. We establish the existence of traveling wavefronts with a minimal wave speed and discuss the selection of wave profiles supplemented with numerical simulations illustrating the wave patterns which are well consistent with experimental observations.
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Taxonomy
TopicsMathematical Biology Tumor Growth · Mathematical and Theoretical Epidemiology and Ecology Models · Advanced Mathematical Modeling in Engineering