Lifespan for a semilinear pseudo-parabolic equation.

This paper deals with the blow-up solution to the following semilinear pseudo-parabolic equation ut = Δut +Δu + |u|p−1u {1 < p < +∞, if n = 1, 2; 1 < p ≤ n+2 / n−2 , if n ≥ 3, and the lifespan for the initial energy J(u0) < 0 is considered. This paper generalizes the above results on the following two aspects: 1. a new blow-up condition is given, which holds for all p > 1; 2. a new lifespan is given, which holds for all p > 1 and possible J(u0) ≥ 0. Moreover, as a by product, we refine the lifespan when J(u0) < 0. [ABSTRACT FROM AUTHOR]