This paper deals with a parabolic-parabolic-ODE chemotaxis haptotaxis system with nonlinear diffusion ut = ∇ • (ϕ(u)∇u) − χ∇ • (u∇v) − ξ∇ • (u∇w) + µu(1 − u − w), vt = ∆v − v + u, wt = −vw, under Neumann boundary conditions in a smooth bounded domain Ω ⊂ R 2 , where χ, ξ and µ are positive parameters and ϕ(u) is a nonlinear diffusion function. Firstly, under the case of non-degenerate diffusion, it is proved that the corresponding initial boundary value problem possesses a unique global classical solution that is uniformly bounded in Ω×(0, ∞). Moreover, under the case of degenerate diffusion, we prove that the corresponding problem admits at least one nonnegative global bounded-in-time weak solution. Finally, under some additional conditions, we derive the temporal decay estimate of w.
Please cite this article in press as: P. Zheng et al., Boundedness of solutions in a chemotaxis system with nonlinear sensitivity and logistic source,
AbstractThis paper deals with a parabolic-elliptic chemotaxis system with nonlinear sensitivity and logistic sourceunder homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂ R n (n ≥ 1), where χ > 0, the function ψ(u) is the chemotactic sensitivity, g(u)is the production rate of the chemoattractant and f (u) is the logistic source. Under some suitable assumptions on the nonlinearities ψ(u), g (u) and logistic source f (u), we study the global boundedness of solutions for the problem.
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