Absence of critical mass phenomena in 1D critical quasilinear Keller-Segel systems for m ≤ -1, with all solutions globally bounded.
Ignacio Tello and Michael Winkler,A chemotaxis system with logistic source, Comm
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For the given chemotaxis model, uniform persistence holds when m ≥ 1; the positive equilibrium is linearly stable for χ0 below a parameter-dependent threshold χ*(u*) and unstable above it, with exponential convergence under stated conditions.
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Chemotaxis models with signal-dependent sensitivity and a logistic-type source, II: Persistence and stabilization
For the given chemotaxis model, uniform persistence holds when m ≥ 1; the positive equilibrium is linearly stable for χ0 below a parameter-dependent threshold χ*(u*) and unstable above it, with exponential convergence under stated conditions.