Blow-up upper and lower bounds for solutions of a class of higher order nonlinear pseudo-parabolic equations

Abstract

In this paper, we study the initial boundary value problem for a class of higher-order nonlinear pseudo-parabolic equations with a memory term. First, the blow-up results of the solution when the initial energy is negative or positive are obtained by using concavity analysis, and an upper bound on the blow-up time $ T^* $ is given. Second, a lower bound on the blow-up time $ T^* $ is obtained by applying differential inequalities when the solutions blow up.

Keywords

• higher order pseudo-parabolic equation
• memory term
• blow-up
• upper bound
• lower bound