Blow-up phenomena for a doubly degenerate equation with positive initial energy

Abstract

In this paper, an initial boundary value problem related to the equation u t − div ( | ∇ u m | p − 2 ∇ u m ) = f ( u ) is studied. Under suitable conditions on f , we establish a blow-up result for certain solution with positive initial energy. And blow-up time will be also considered by using the differential inequality technique. The upper estimate of the blow-up solution near the single blow-up point is also obtained.