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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 $$ \left\{ \begin{arra…
math.PR2026
Two-time spatial decorrelation for the flat KPZ fixed point
Le Chen, Fei Pu
We establish quantitative two-time spatial decorrelation for the Kardar--Parisi--Zhang fixed point with flat initial data. For every ,there exist constants such that…
math.AP2026
Chemotaxis models with signal-dependent sensitivity and a logistic-type source, II: Persistence and stabilization
Le Chen, Ian Ruau, Wenxian Shen
This paper is Part II of a series on boundedness, global existence, and asymptotic behavior of positive classical solutions to the chemotaxis model $$\begin{cases} u_t=Δu-χ_0\nabla…