Blow-Up Phenomena for a Sixth-Order Partial Differential Equation with a General Nonlinearity

In this paper, we study the blow-up results for the sixth-order time-dependent partial differential equation (PDE). First, we establish the existence of global solutions for the given equation with the help of the Dirichlet-Neumann type boundary conditions. Moreover, we derive an upper bound for the blow-up time of the solution. Finally, we also obtain a lower bound for the blow-up time of the solution using the first-order differential inequality technique when blow-up occurs.