Blow-up for a degenerate parabolic equation with a nonlocal source

In this paper existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution that exists globally or blows up in finite time are obtained for the degenerate parabolic problemxqut-uxx=∫0aum(x,t)dx-kun(x,t),in(0,a)×(0,T),where 00,m⩾n>1,k>0 are constants.