3 papers
math.AP2026
Chemotaxis models with signal-dependent sensitivity and a logistic-type source, III: Bifurcation and spike-like solutions
Le Chen, Ian Ruau, Wenxian Shen
This third paper in a series on a parabolic-elliptic chemotaxis model studies bifurcation of positive constant equilibria in one space dimension. We consider $$ \left\{ \begin{arra…
math.AP2026
Chemotaxis models with signal-dependent sensitivity and a logistic-type source, II: Persistence and stabilization
Le Chen, Ian Ruau, Wenxian Shen
This paper is Part II of a series on boundedness, global existence, and asymptotic behavior of positive classical solutions to the chemotaxis model $$\begin{cases} u_t=Δu-χ_0\nabla…
math.AP2025
Chemotaxis models with signal-dependent sensitivity and a logistic-type source, I: Boundedness and global existence
Le Chen, Ian Ruau, Wenxian Shen
We study, in Part I of this series, boundedness and global existence of positive classical solutions to a parabolic-elliptic chemotaxis system with signal-dependent sensitivity and…