Bounds on blow-up time for a pseudo-parabolic equation with a memory term

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In this paper, we study the initial boundary value problem for a class of semilinear pseudo-parabolic equation with a memory term. By the means of the differential inequality technique, we obtain a lower bound for blow-up time of the solution if blow-up occurs. At the same time, we establish a blow-up criterion and give an upper bound for blow-up time of the solution under some conditions on initial data.