Upper and lower bounds of blow-up time for a class of semi-linear pseudo-parabolic equation

In this paper, the blow-up phenomena of a class of semi-linear pseudo-parabolic equations are studied, the estimation of upper and lower bounds of blow-up time under different initial conditions are given. To be specific, the lower bound of blow-up time under low initial energy is obtained by the means of using differential inequality technique, and the lower bound of blow-up time under high initial energy is obtained similarly. Then, the upper bound of blow-up time under any initial energy is obtained by the means of using convex method.