Blow-Up Phenomena for a Fourth-Order Parabolic Equation with a General Nonlinearity

This paper is concerned with the blow-up property of solutions to an initial boundary value problem for a fourth-order parabolic equation with a general nonlinearity. It is shown, under certain conditions on the initial data, that the solutions to this problem blow up in finite time, using differential inequalities. Moreover, upper and lower bounds for the blow-up time are derived when blow-up occurs. This extends and generalizes results obtained by Philippin (Proc AMS. 2015;143(6):2507–13) and by Han (Nonlinear Anal RWA. 2018;43:451–66).