Blow-Up of the Solution of the Initial Boundary-Value Problem for the Generalized Boussinesq Equation with Nonlinear Boundary Condition

The initial boundary-value problem for a nonlinear equation of pseudoparabolic type with nonlinear Neumann boundary condition is considered. We prove a local theorem on the existence of solutions. Using the method of energy inequalities, we obtain sufficient conditions for the blow-up of solutions in a finite time interval and establish upper and lower bounds for the blow-up time.