Abstract This work considers a chemotaxis system with signal-dependent motility in a smooth bounded domain Ω ⊂ R n . If λ ∈ R , μ > 0 and l > max ⁡ { n + 2 4 , 1 } are constants, then the system { u t = Δ ( γ ( v ) u ) + λ u − μ u l , x ∈ Ω , t > 0 , v t = Δ v − v + w , x ∈ Ω , t > 0 , w t = Δ w − w + u , x ∈ Ω , t > 0 , with homogeneous Neumann boundary conditions possesses a global solution. Moreover, the solution satisfies ‖ u ( ⋅ , t ) − ( λ + μ ) 1 l − 1 ‖ L ∞ + ‖ v ( ⋅ , t ) − ( λ + μ ) 1 l − 1 ‖ L ∞ + ‖ w ( ⋅ , t ) − ( λ + μ ) 1 l − 1 ‖ L ∞ → 0 as t → ∞ under some extra hypotheses, where λ + = max ⁡ { λ , 0 } .

中文翻译：

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具有信号依赖性运动、间接信号产生和广义逻辑源的趋化系统：全局存在和渐近稳定

摘要 这项工作考虑了在光滑有界域Ω ⊂ R n 中具有信号依赖运动的趋化系统。如果 λ ∈ R , μ > 0 和 l > max ⁡ { n + 2 4 , 1 } 是常数，则系统 { ut = Δ ( γ ( v ) u ) + λ u − μ ul , x ∈ Ω , t > 0 , vt = Δ v − v + w , x ∈ Ω , t > 0 , wt = Δ w − w + u , x ∈ Ω , t > 0 ，齐次 Neumann 边界条件具有全局解。此外，解满足 ‖ u ( ⋅ , t ) − ( λ + μ ) 1 l − 1 ‖ L ∞ + ‖ v ( ⋅ , t ) − ( λ + μ ) 1 l − 1 ‖ L ∞ + ‖ w ( ⋅ , t ) − ( λ + μ ) 1 l − 1 ‖ L ∞ → 0 as t → ∞ 在一些额外的假设下，其中 λ + = max ⁡ { λ , 0 } 。