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

In this paper, we investigate the blowup properties of the positive solutions to the following nonlocal degenerate parabolic equation vτ = xα(vm)xx + l 0 vp1 dx − kvq1 with homogeneous Dirichlet boundary conditions in the interval (0, l), where 0<α <2, p1 q1 > m>1. We first establish the local existence and uniqueness of its classical solutions. Then we show that the positive solution blows up in finite time if the initial datum is sufficient large. Finally, we prove that the blow-up set is the whole interval and we also obtain the estimates of the blow-up rate.  2003 Elsevier Inc. All rights reserved.