Blow-up for a nonlocal parabolic equation Original Research Article

In this paper, we consider the blow-up properties of the radial solutions of the nonlocal parabolic equation View the MathML sourceut=Δu+λuα(∫B1(u+1)−αdx)p,x∈B1,t>0, Turn MathJax on with homogeneous Dirichlet boundary condition, where λ,p>0λ,p>0, 0<α≤10<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<10<α<1, global and nonuniform for α=1α=1. The blow-up rate of |u|∞|u|∞ is also determined.