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This paper deals with the attraction‐repulsion chemotaxis system with logistic source
under homogeneous Neumann boundary conditions in a smooth bounded domain . Under a growth restriction on logistic source and suitable assumptions on the positive parameters χ, ξ, α, β, γ and δ, we show the existence of global bounded classical solutions. The global weak solution is also constructed if the...
In this paper, we consider the blow-up properties of the radial solutions of the nonlocal parabolic equation ut=Δu+λuα(∫B1(u+1)−αdx)p,x∈B1,t>0, with homogeneous Dirichlet boundary condition, where λ,p>0, 0<α≤1. The criteria for the solutions to blow-up in finite time is given. It is proved that the blow-up is global and uniform for 0<α<1, global and nonuniform for α=1. The blow-up rate...
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