Stabilization in the Keller–Segel system with signal-dependent sensitivity. Issue 16 (9th December 2020) - Black, Tobias; Lankeit, Johannes; Mizukami, Masaaki
Abstract : This paper deals with the Keller–Segel system with signal-dependent sensitivity u t = Δ u − χ ∇ ⋅ ( u S ( v ) ∇ v ), v t = Δ v − v + u, where χ > 0 and S is a given function generalizing the sensitivity S ( s ) = 1 / ( a + s ) k, k >1, a ≥ 0, and shows exponential convergence of global classical solutions under an additional smallness condition for χ > 0 .