Existence and asymptotic behavior of global solutions to chemorepulsion systems with nonlinear sensitivity
Texas State University, Department of Mathematics
This 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.
Chemotaxis, Repulsion, Nonlinear sensitivity, Global solution, Asymptotic behavior
Lai, 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.