Resumen de Boundedness in a Two-Species Chemotaxis System with Nonlinear Resource Consumption

Houzuo Ou, Liangchen Wang

• This paper deals with a two-species chemotaxis system with nonlinear resource consumption ⎧ ⎪⎪⎨ ⎪⎪⎩ ut = u −∇· (u∇w) + μ1u(1 − u − a1v), x ∈ , t > 0, vt = v −∇· (v∇w) + μ2v(1 − a2u − v), x ∈ , t > 0, wt = w − (u + v)w (1 + u + v)θ , x ∈ , t > 0 under homogeneous Neumann boundary conditions in a smooth bounded domain ⊂ Rn(n ≥ 1), where the parameters μ1, μ2, a1, a2 > 0. For all suitably regular initial data, we prove that if θ > 0, the system possesses a unique global bounded classical solution.