Abstract
This paper deals with the initial value problem for a parabolic attraction-repulsion chemotaxis system in R2:{∂tu=Δu−∇⋅(u∇(β1v1−β2v2)),t>0,x∈R2,∂tvj=Δvj−λjvj+u,t>0,x∈R2(j=1,2),u(0,x)=u0(x),vj(0,x)=vj0(x),x∈R2(j=1,2) with positive parameters β1, β2, λ1, λ2 and nonnegative initial data u0, v10, v20. It is well known that the sign of β1−β2 and the mass on u0 play a crucial role in the global boundedness of the system. Specifically, in the attractive dominant case β1>β2, the uniform boundedness of nonnegative solutions has been guaranteed under the condition ∫R2u0dx<4π. Also, in the balance case β1=β2, it has been proven that every nonnegative solution is bounded uniformly in time without any restriction on the mass u0. In this paper, we discuss the global existence and boundedness of nonnegative solutions to the system in the repulsive dominant case β1<β2.
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