DYNAMICS FOR A CHEMOTAXIS MODEL WITH GENERAL LOGISTIC DAMPING AND SIGNAL DEPENDENT MOTILITY

In this paper,we consider the fully parabolic chemotaxis system with the general logistic source■ where Ω C Rn(n ≥ 1) is a smooth and bounded domain,λ≥ 0,μ≥ 0,κ> 1,and the motility function satisfies that γ(v) E C3([0,∞)),γ(v) 0,γ’(v)≤0 for all v≥0.Considering the Neumann boundary condition,we obtain the global boundedness of solutions if one of the following conditions holds:(ⅰ) κ=μ=0,1 ≤n ≤3;(ⅱ) λ> 0,μ> 0,combined with κ> 1,1 ≤n≤3 or κ>(n+2)/4,n> 3.Moreover,we prove that the solution(u,v,w,z) exponentially converges to the constant steady state■.