EXISTENCE AND ASYMPTOTIC BEHAVIOR OF GLOBAL SOLUTIONS TO CHEMOREPULSION SYSTEMS WITH NONLINEAR SENSITIVITY.

This article concerns the chemorepulsion system with nonlinear sensitivity and nonlinear secretion ut = Δu + ▿ u (χum▿v), x ∊Ω , t > 0; 0 = Δv -- v + uα, 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 (¯u0; ¯uα0 ) as time goes to infinity, where ¯u0 := 1 |Ω |∫ Ω u0dx. [ABSTRACT FROM AUTHOR]