The Blow-Up Rate for a Degenerate Parabolic Equation with a Non-local Source

In this paper, we establish the local existence of the solution and the finite time blow-up result for the equation Ž m. aHl qdx, x Ž l, l., 0. x x l Moreover, it is proved that the solution has global blow-up, and there exist constants C1 , C 2 such that C1 ŽT1 . 1 Žq 1. max Žx, . C 2ŽT1 . 1 Žq 1., x l , l where T1 is the blow-up time.