Lai, YulinXiao, Youjun2022-08-082022-08-082017-10-10Lai, Y., & Xiao, Y. (2017). Existence and asymptotic behavior of global solutions to chemorepulsion systems with nonlinear sensitivity. <i>Electronic Journal of Differential Equations, 2017</i>(254), pp. 1-9.1072-6691https://hdl.handle.net/10877/16048This article concerns the chemorepulsion system with nonlinear sensitivity and nonlinear secretion ut = ∆u + ∇ ∙ (χum∇v), x ∈ Ω, t > 0, 0 = ∆v - v + uα, x x ∈ Ω, t > 0, under homogeneous Neumann boundary conditions, where χ > 0, m > 0, α > 0, Ω ⊂ ℝn is a bounded domain with smooth boundary. The existence and uniform boundedness of a classical global solutions are obtained. Furthermore, it is shown that for any given u0, if α > m or α ≥ 1, the corresponding solution (u, v) converges to (ū0, ūα0) as time goes to infinity, where ū0 ≔ 1/|Ω| ∫Ω u0dx.Text9 pages1 file (.pdf)enAttribution 4.0 InternationalChemotaxisRepulsionNonlinear sensitivityGlobal solutionAsymptotic behaviorArticle